prompt stringlengths 195 3.01k | vanilla_response stringlengths 35 75.4k | question stringlengths 16 2.83k | answer stringlengths 2 3.48k | question_id int64 0 3.19k | generation_id int64 0 255 | response stringlengths 35 75.4k | label bool 2
classes | gold_answer stringlengths 1 47 | pred_answer stringlengths 0 66.3k |
|---|---|---|---|---|---|---|---|---|---|
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will break it down into steps.
## Step 1: Define the variables
Let's define the variables:
- $s$ as Aya's constant speed in kilometers per hour when walking alone.
- $t$ as the time in minutes Aya spends in the coffee shop.
- $s + \frac{1}{2}$ as the speed in kilometers per hour when Aya walk... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 0 | To solve this problem, we will break it down into steps.
## Step 1: Define the variables
Let's define the variables:
- $s$ as Aya's constant speed in kilometers per hour when walking alone.
- $t$ as the time in minutes Aya spends in the coffee shop.
- $s + \frac{1}{2}$ as the speed in kilometers per hour when Aya walk... | false | 204 | 292 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to break it down into steps.
## Step 1: First, let's establish the relationship between the distance, speed, and time for Aya's walk.
The distance of the walk is given as 9 kilometers. We have two scenarios with different speeds and times, which will allow us to create equations to solve... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 1 | To solve this problem, we need to break it down into steps.
## Step 1: First, let's establish the relationship between the distance, speed, and time for Aya's walk.
The distance of the walk is given as 9 kilometers. We have two scenarios with different speeds and times, which will allow us to create equations to solve... | false | 204 | 140.76 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to first convert all the times to the same units. We are given that the walk takes her 4 hours, including $t$ minutes spent in the coffee shop when she walks at a constant speed of $s$ kilometers per hour. We can convert 4 hours to minutes by multiplying by 60:
\[4\text{ hours}\cdot 60\t... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 2 | To solve this problem, we need to first convert all the times to the same units. We are given that the walk takes her 4 hours, including $t$ minutes spent in the coffee shop when she walks at a constant speed of $s$ kilometers per hour. We can convert 4 hours to minutes by multiplying by 60:
\[4\text{ hours}\cdot 60\t... | false | 204 | 64 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, let's break it down into steps.
## Step 1: Understand the problem
We are given that Aya goes for a 9-kilometer-long walk and then stops at a coffee shop. We need to find the time it takes her to walk 9 kilometers at a speed of $s+\frac{1}{2}$ kilometers per hour, including the time spent in the... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 3 | To solve this problem, let's break it down into steps.
## Step 1: Understand the problem
We are given that Aya goes for a 9-kilometer-long walk and then stops at a coffee shop. We need to find the time it takes her to walk 9 kilometers at a speed of $s+\frac{1}{2}$ kilometers per hour, including the time spent in the... | false | 204 | 214.29 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow the steps below:
## Step 1: First, we need to establish the relationship between Aya's walking speed and the time she spends walking and at the coffee shop.
Let's denote the time spent walking at the initial speed $s$ as $4 - t/60$ hours, and the time spent walking at the speed $... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 4 | To solve this problem, we will follow the steps below:
## Step 1: First, we need to establish the relationship between Aya's walking speed and the time she spends walking and at the coffee shop.
Let's denote the time spent walking at the initial speed $s$ as $4 - t/60$ hours, and the time spent walking at the speed $... | false | 204 | 527 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first need to convert all the given times into minutes.
## Step 1: Convert the time from hours to minutes
We know that 4 hours is equal to 4 * 60 = 240 minutes.
## Step 2: Convert 2 hours and 24 minutes to minutes
We know that 2 hours is equal to 2 * 60 = 120 minutes. Therefore, 2 hours... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 5 | To solve this problem, we will first need to convert all the given times into minutes.
## Step 1: Convert the time from hours to minutes
We know that 4 hours is equal to 4 * 60 = 240 minutes.
## Step 2: Convert 2 hours and 24 minutes to minutes
We know that 2 hours is equal to 2 * 60 = 120 minutes. Therefore, 2 hours... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Convert given times to just hours for consistency
First, we need to convert the time given in the second scenario into just hours. 2 hours and 24 minutes is equivalent to $2 + \frac{24}{60} = 2.4$ hours.
## Step 2: Set up equations based on the given i... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 6 | To solve this problem, we'll break it down into steps.
## Step 1: Convert given times to just hours for consistency
First, we need to convert the time given in the second scenario into just hours. 2 hours and 24 minutes is equivalent to $2 + \frac{24}{60} = 2.4$ hours.
## Step 2: Set up equations based on the given i... | false | 204 | 198 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first convert all the times to just hours and then set up an equation to solve for $t$.
When Aya walks at a constant speed of $s$ kilometers per hour, the walk takes her $4$ hours, including $t$ minutes spent in the coffee shop. Since $t$ is in minutes, we need to convert it to hours. We... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 7 | To solve this problem, we will first convert all the times to just hours and then set up an equation to solve for $t$.
When Aya walks at a constant speed of $s$ kilometers per hour, the walk takes her $4$ hours, including $t$ minutes spent in the coffee shop. Since $t$ is in minutes, we need to convert it to hours. We... | false | 204 | 920 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time it takes for Aya to walk 9 kilometers at speed $s$ as $t_1$ hours, and the time spent in the coffee shop as $t$ minutes. We can convert $t$ to hours by dividing by 60: $t = \frac{t}{60}$ hours.
When Aya w... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 8 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time it takes for Aya to walk 9 kilometers at speed $s$ as $t_1$ hours, and the time spent in the coffee shop as $t$ minutes. We can convert $t$ to hours by dividing by 60: $t = \frac{t}{60}$ hours.
When Aya w... | false | 204 | 54 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Understand the given problem and define the variables
We are given that Aya walks at a speed of $s$ kilometers per hour and covers a distance of $9$ kilometers. The total time taken for the walk and the time spent in the coffee shop is given as $4$ hour... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 9 | To solve this problem, we'll break it down into steps.
## Step 1: Understand the given problem and define the variables
We are given that Aya walks at a speed of $s$ kilometers per hour and covers a distance of $9$ kilometers. The total time taken for the walk and the time spent in the coffee shop is given as $4$ hour... | false | 204 | 14160 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
First, let's convert the time spent walking into hours for both scenarios:
- At $s$ kilometers per hour, the walk takes 4 hours, which is $\frac{4}{60} = \frac{1}{15}$ hours longer than the time spent in the coffee shop. So, th... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 10 | To solve this problem, we can start by setting up equations based on the information given.
First, let's convert the time spent walking into hours for both scenarios:
- At $s$ kilometers per hour, the walk takes 4 hours, which is $\frac{4}{60} = \frac{1}{15}$ hours longer than the time spent in the coffee shop. So, th... | false | 204 | 364 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll first establish the equations based on the information given and then solve for the unknowns.
Given:
- Aya walks 9 kilometers.
- At speed $s$ km/h, the walk takes 4 hours, including $t$ minutes in the coffee shop.
- At speed $s+2$ km/h, the walk takes 2 hours and 24 minutes, including $t$ ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 11 | To solve this problem, we'll first establish the equations based on the information given and then solve for the unknowns.
Given:
- Aya walks 9 kilometers.
- At speed $s$ km/h, the walk takes 4 hours, including $t$ minutes in the coffee shop.
- At speed $s+2$ km/h, the walk takes 2 hours and 24 minutes, including $t$ ... | false | 204 | 5963.5 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time it takes for Aya to walk 9 kilometers at speed $s$ as $t_{walk}$ and the time she spends in the coffee shop as $t$. We know that the total time for the walk at speed $s$ is 4 hours, including $t$ minutes s... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 12 | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time it takes for Aya to walk 9 kilometers at speed $s$ as $t_{walk}$ and the time she spends in the coffee shop as $t$. We know that the total time for the walk at speed $s$ is 4 hours, including $t$ minutes s... | false | 204 | 14326 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll start by setting up equations based on the information given.
Let's denote:
- $s$ as Aya's walking speed in kilometers per hour.
- $t$ as the time spent in the coffee shop in minutes.
From the given information, we have two equations:
1. When Aya walks at a constant speed of $s$ kilomete... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 13 | To solve this problem, we'll start by setting up equations based on the information given.
Let's denote:
- $s$ as Aya's walking speed in kilometers per hour.
- $t$ as the time spent in the coffee shop in minutes.
From the given information, we have two equations:
1. When Aya walks at a constant speed of $s$ kilomete... | false | 204 | 240 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to first find the value of t, then use it to calculate the time taken for the walk at s + 0.5 km/h.
## Step 1: Set up the equations based on the given information.
When Aya walks at s kilometers per hour, the total time taken is 4 hours, which is equal to 240 minutes. This includes t min... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 14 | To solve this problem, we need to first find the value of t, then use it to calculate the time taken for the walk at s + 0.5 km/h.
## Step 1: Set up the equations based on the given information.
When Aya walks at s kilometers per hour, the total time taken is 4 hours, which is equal to 240 minutes. This includes t min... | false | 204 | 11804 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will break it down into steps.
## Step 1: Define the variables and establish the equations based on the information given.
Let's denote the time spent walking at the initial speed $s$ kilometers per hour as $t_1$ hours and the time spent walking at the increased speed $s+2$ kilometers per hou... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 15 | To solve this problem, we will break it down into steps.
## Step 1: Define the variables and establish the equations based on the information given.
Let's denote the time spent walking at the initial speed $s$ kilometers per hour as $t_1$ hours and the time spent walking at the increased speed $s+2$ kilometers per hou... | false | 204 | 56.875 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Understand the given information
We have two scenarios:
- When Aya walks at a speed of $s$ kilometers per hour, the total time taken for the walk and coffee is 4 hours, including $t$ minutes spent in the coffee shop.
- When Aya walks at a speed of $s+2$... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 16 | To solve this problem, we'll break it down into steps.
## Step 1: Understand the given information
We have two scenarios:
- When Aya walks at a speed of $s$ kilometers per hour, the total time taken for the walk and coffee is 4 hours, including $t$ minutes spent in the coffee shop.
- When Aya walks at a speed of $s+2$... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, let's break it down into steps.
## Step 1: Understand the given information
We are given that Aya walks 9 kilometers, and the time taken for the walk changes based on her speed. We have two scenarios:
- When she walks at $s$ kilometers per hour, the total time taken is 4 hours, including $t$ min... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 17 | To solve this problem, let's break it down into steps.
## Step 1: Understand the given information
We are given that Aya walks 9 kilometers, and the time taken for the walk changes based on her speed. We have two scenarios:
- When she walks at $s$ kilometers per hour, the total time taken is 4 hours, including $t$ min... | false | 204 | 240 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to first determine the value of $t$ and then find the time it takes for Aya to walk at a speed of $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Convert the time spent walking and the time spent in the coffee shop into hours.
First, let's convert 4 hours into minutes. 4 hours * 60 minu... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 18 | To solve this problem, we need to first determine the value of $t$ and then find the time it takes for Aya to walk at a speed of $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Convert the time spent walking and the time spent in the coffee shop into hours.
First, let's convert 4 hours into minutes. 4 hours * 60 minu... | false | 204 | 84.5 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Understand the problem
Aya walks 9 kilometers, and we're given two scenarios: one where she walks at a speed of $s$ km/h and takes 4 hours, including $t$ minutes in the coffee shop, and another where she walks at a speed of $s+2$ km/h and takes 2 hours ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 19 | To solve this problem, we'll break it down into steps.
## Step 1: Understand the problem
Aya walks 9 kilometers, and we're given two scenarios: one where she walks at a speed of $s$ km/h and takes 4 hours, including $t$ minutes in the coffee shop, and another where she walks at a speed of $s+2$ km/h and takes 2 hours ... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking at $s$ km/h as $w$ hours and the time she spends walking at $s+2$ km/h as $w'$ hours. Since she spends $t$ minutes in the coffee shop, we can express the time spent in the coffee shop in... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 20 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking at $s$ km/h as $w$ hours and the time she spends walking at $s+2$ km/h as $w'$ hours. Since she spends $t$ minutes in the coffee shop, we can express the time spent in the coffee shop in... | false | 204 | 216 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow these steps:
## Step 1: Set up the first equation
First, let's calculate the time Aya takes to walk 9 kilometers at a speed of $s$ kilometers per hour. Time is equal to distance divided by speed, so the time taken for the walk is $\frac{9}{s}$ hours. We know that this time, includ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 21 | To solve this problem, we will follow these steps:
## Step 1: Set up the first equation
First, let's calculate the time Aya takes to walk 9 kilometers at a speed of $s$ kilometers per hour. Time is equal to distance divided by speed, so the time taken for the walk is $\frac{9}{s}$ hours. We know that this time, includ... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to find the value of $s$ and then calculate the time it takes Aya to walk 9 kilometers at a speed of $s + \frac{1}{2}$ kilometers per hour.
## Step 1: Convert the given times into just hours
We have two scenarios:
- When Aya walks at a constant speed of $s$ kilometers per hour, the walk ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 22 | To solve this problem, we need to find the value of $s$ and then calculate the time it takes Aya to walk 9 kilometers at a speed of $s + \frac{1}{2}$ kilometers per hour.
## Step 1: Convert the given times into just hours
We have two scenarios:
- When Aya walks at a constant speed of $s$ kilometers per hour, the walk ... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to break it down into steps.
## Step 1: Define the variables and the given information
Let $s$ be Aya's walking speed in kilometers per hour, and $t$ be the time in minutes she spends in the coffee shop.
## Step 2: Convert the time from hours to minutes for both walking speeds
When she ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 23 | To solve this problem, we need to break it down into steps.
## Step 1: Define the variables and the given information
Let $s$ be Aya's walking speed in kilometers per hour, and $t$ be the time in minutes she spends in the coffee shop.
## Step 2: Convert the time from hours to minutes for both walking speeds
When she ... | false | 204 | 1056 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to break it down into smaller steps.
## Step 1: Understand the problem
We are given that Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. We need to find the time it takes her to complete the walk when she walks at a speed of $s+\frac{1}{2}$ kilometers per ho... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 24 | To solve this problem, we need to break it down into smaller steps.
## Step 1: Understand the problem
We are given that Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. We need to find the time it takes her to complete the walk when she walks at a speed of $s+\frac{1}{2}$ kilometers per ho... | false | 204 | 106\frac{ |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first set up equations based on the information given and then solve for the unknowns.
Let's denote the time Aya takes to walk 9 kilometers at her constant speed $s$ kilometers per hour as $t_{\text{walk}}$ and the time she spends in the coffee shop as $t$. We are given two scenarios:
1... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 25 | To solve this problem, we will first set up equations based on the information given and then solve for the unknowns.
Let's denote the time Aya takes to walk 9 kilometers at her constant speed $s$ kilometers per hour as $t_{\text{walk}}$ and the time she spends in the coffee shop as $t$. We are given two scenarios:
1... | false | 204 | 239 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to first determine the value of \( s \), the speed at which Aya walks when the walk takes her 4 hours, including \( t \) minutes spent in the coffee shop. Then, we will calculate the time taken for the walk at the speed \( s + \frac{1}{2} \) kilometers per hour.
## Step 1: Convert the ti... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 26 | To solve this problem, we need to first determine the value of \( s \), the speed at which Aya walks when the walk takes her 4 hours, including \( t \) minutes spent in the coffee shop. Then, we will calculate the time taken for the walk at the speed \( s + \frac{1}{2} \) kilometers per hour.
## Step 1: Convert the ti... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that when she walks at a speed of $s$ kilometers per hour, the total time taken is 4 hours, including $t$ ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 27 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that when she walks at a speed of $s$ kilometers per hour, the total time taken is 4 hours, including $t$ ... | false | 204 | 27 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: First, let's establish the equations based on the information given for the two walking speeds.
When Aya walks at speed $s$ kilometers per hour, the total time taken for the walk and coffee is 4 hours, which is equivalent to 240 minutes. This includes t... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 28 | To solve this problem, we'll break it down into steps.
## Step 1: First, let's establish the equations based on the information given for the two walking speeds.
When Aya walks at speed $s$ kilometers per hour, the total time taken for the walk and coffee is 4 hours, which is equivalent to 240 minutes. This includes t... | false | 204 | 28707 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Convert the given times to a common unit
First, let's convert all the given times into minutes. The first walk takes 4 hours, which is $4 \times 60 = 240$ minutes, including $t$ minutes spent in the coffee shop. The second walk takes 2 hours and 24 minu... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 29 | To solve this problem, we'll break it down into steps.
## Step 1: Convert the given times to a common unit
First, let's convert all the given times into minutes. The first walk takes 4 hours, which is $4 \times 60 = 240$ minutes, including $t$ minutes spent in the coffee shop. The second walk takes 2 hours and 24 minu... | false | 204 | 578.79 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that the total time for the walk is 4 hours when she walks at a speed of $s$ kilometers per hour, and 2 ho... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 30 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that the total time for the walk is 4 hours when she walks at a speed of $s$ kilometers per hour, and 2 ho... | false | 204 | 240 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, let's break it down into steps.
Step 1: Convert the time from hours and minutes to just minutes for easier calculation.
4 hours = 240 minutes
2 hours 24 minutes = 144 minutes + 24 minutes = 168 minutes
Step 2: Set up the equation for the first scenario, where Aya walks at s kilometers per hour.... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 31 | To solve this problem, let's break it down into steps.
Step 1: Convert the time from hours and minutes to just minutes for easier calculation.
4 hours = 240 minutes
2 hours 24 minutes = 144 minutes + 24 minutes = 168 minutes
Step 2: Set up the equation for the first scenario, where Aya walks at s kilometers per hour.... | false | 204 | 648 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will break it down into steps.
## Step 1: Understand the problem and define the variables.
We have three different speeds at which Aya walks: $s$ kilometers per hour, $s+2$ kilometers per hour, and $s+\frac{1}{2}$ kilometers per hour. The distance of the walk is always 9 kilometers. We need ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 32 | To solve this problem, we will break it down into steps.
## Step 1: Understand the problem and define the variables.
We have three different speeds at which Aya walks: $s$ kilometers per hour, $s+2$ kilometers per hour, and $s+\frac{1}{2}$ kilometers per hour. The distance of the walk is always 9 kilometers. We need ... | false | 204 | 3.4 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow these steps:
## Step 1: Define the variables and the equations
Let's define the variables and the equations based on the information given in the problem. We know that Aya walks 9 kilometers, and the time taken is 4 hours when she walks at a speed of $s$ km/h, and 2 hours and 24 m... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 33 | To solve this problem, we will follow these steps:
## Step 1: Define the variables and the equations
Let's define the variables and the equations based on the information given in the problem. We know that Aya walks 9 kilometers, and the time taken is 4 hours when she walks at a speed of $s$ km/h, and 2 hours and 24 m... | false | 204 | 316 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to determine the value of \( s \) and then calculate the time taken for the walk at the speed \( s + \frac{1}{2} \) kilometers per hour.
## Step 1: Convert the given times into a common unit
First, convert the times into hours for consistency. The first scenario takes 4 hours, which is e... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 34 | To solve this problem, we need to determine the value of \( s \) and then calculate the time taken for the walk at the speed \( s + \frac{1}{2} \) kilometers per hour.
## Step 1: Convert the given times into a common unit
First, convert the times into hours for consistency. The first scenario takes 4 hours, which is e... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow these steps:
## Step 1: Define the variables and understand the problem
Let's denote the time Aya spends walking at speed $s$ kilometers per hour as $t_1$ hours and the time she spends walking at speed $s+2$ kilometers per hour as $t_2$ hours. We are given that $t_1 = 4 - \frac{t}... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 35 | To solve this problem, we will follow these steps:
## Step 1: Define the variables and understand the problem
Let's denote the time Aya spends walking at speed $s$ kilometers per hour as $t_1$ hours and the time she spends walking at speed $s+2$ kilometers per hour as $t_2$ hours. We are given that $t_1 = 4 - \frac{t}... | false | 204 | 305\frac{11}{31} |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first convert the given times into hours, then set up equations based on the distance and speed information, and finally solve for the time spent walking.
## Step 1: Convert the given times into hours
We are given that when Aya walks at $s$ kilometers per hour, the walk takes her 4 hours... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 36 | To solve this problem, we will first convert the given times into hours, then set up equations based on the distance and speed information, and finally solve for the time spent walking.
## Step 1: Convert the given times into hours
We are given that when Aya walks at $s$ kilometers per hour, the walk takes her 4 hours... | false | 204 | 237.17 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first set up equations based on the information given. Let's denote the time it takes for Aya to walk 9 kilometers at her normal speed $s$ as $t_{\text{walk}}$ and the time spent in the coffee shop as $t$.
When Aya walks at a constant speed of $s$ kilometers per hour, the walk takes her ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 37 | To solve this problem, we will first set up equations based on the information given. Let's denote the time it takes for Aya to walk 9 kilometers at her normal speed $s$ as $t_{\text{walk}}$ and the time spent in the coffee shop as $t$.
When Aya walks at a constant speed of $s$ kilometers per hour, the walk takes her ... | false | 204 | 16 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow these steps:
## Step 1: Define the given information
Aya walks 9 kilometers, and the time it takes her to walk this distance changes based on her speed. When she walks at a speed of s kilometers per hour, the total time taken is 4 hours, including t minutes spent in the coffee sho... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 38 | To solve this problem, we will follow these steps:
## Step 1: Define the given information
Aya walks 9 kilometers, and the time it takes her to walk this distance changes based on her speed. When she walks at a speed of s kilometers per hour, the total time taken is 4 hours, including t minutes spent in the coffee sho... | false | 204 | 69 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking at speed $s$ kilometers per hour as $t_1$ hours and the time she spends walking at speed $s+2$ kilometers per hour as $t_2$ hours. We are given that $t_1 + \frac{t}{60} = 4$ and $t_2 + \... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 39 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking at speed $s$ kilometers per hour as $t_1$ hours and the time she spends walking at speed $s+2$ kilometers per hour as $t_2$ hours. We are given that $t_1 + \frac{t}{60} = 4$ and $t_2 + \... | false | 204 | 50 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can use the formula for time, which is:
Time = Distance / Speed
We are given that Aya walks at two different speeds, s and s+2 kilometers per hour, and we know the time it takes her to complete the walk and spend time in the coffee shop at each speed.
Let's start by using the information th... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 40 | To solve this problem, we can use the formula for time, which is:
Time = Distance / Speed
We are given that Aya walks at two different speeds, s and s+2 kilometers per hour, and we know the time it takes her to complete the walk and spend time in the coffee shop at each speed.
Let's start by using the information th... | false | 204 | 393 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to find the value of $s$ and then use it to calculate the time taken for the walk at $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Let's denote the time spent walking at $s$ kilometers per hour as $t_s$ hours and the time spent walking at $s+2$ kilometers per hour as $t_{s+2}$ hours.
G... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 41 | To solve this problem, we need to find the value of $s$ and then use it to calculate the time taken for the walk at $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Let's denote the time spent walking at $s$ kilometers per hour as $t_s$ hours and the time spent walking at $s+2$ kilometers per hour as $t_{s+2}$ hours.
G... | false | 204 | 196 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll start by setting up equations based on the information given.
Let's denote the time Aya spends walking at a speed of $s$ kilometers per hour as $t_s$ hours and the time she spends walking at a speed of $s+2$ kilometers per hour as $t_{s+2}$ hours. We're given that the total time for each s... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 42 | To solve this problem, we'll start by setting up equations based on the information given.
Let's denote the time Aya spends walking at a speed of $s$ kilometers per hour as $t_s$ hours and the time she spends walking at a speed of $s+2$ kilometers per hour as $t_{s+2}$ hours. We're given that the total time for each s... | false | 204 | 6.6 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down step by step.
Step 1: Define the variables and given information.
- Aya's speed when walking at $s$ kilometers per hour is $s$ km/h.
- The total distance of her walk is 9 kilometers.
- When walking at $s$ km/h, the walk takes her 4 hours, including $t$ minutes spent in the co... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 43 | To solve this problem, we'll break it down step by step.
Step 1: Define the variables and given information.
- Aya's speed when walking at $s$ kilometers per hour is $s$ km/h.
- The total distance of her walk is 9 kilometers.
- When walking at $s$ km/h, the walk takes her 4 hours, including $t$ minutes spent in the co... | false | 204 | 21.54 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first set up equations based on the information given.
Let's denote the time it takes for Aya to walk 9 kilometers at a speed of s kilometers per hour as $t_{\text{walk}}$ and the time she spends in the coffee shop as $t$.
Given that the total time taken for the walk is 4 hours, we can... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 44 | To solve this problem, we will first set up equations based on the information given.
Let's denote the time it takes for Aya to walk 9 kilometers at a speed of s kilometers per hour as $t_{\text{walk}}$ and the time she spends in the coffee shop as $t$.
Given that the total time taken for the walk is 4 hours, we can... | false | 204 | 2 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to find the value of $t$ and then calculate the time it takes Aya to walk at $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Let's denote the time it takes Aya to walk 9 kilometers at speed s kilometers per hour as t + 4 hours.
We know that time equals distance divided by speed. So, the ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 45 | To solve this problem, we need to find the value of $t$ and then calculate the time it takes Aya to walk at $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Let's denote the time it takes Aya to walk 9 kilometers at speed s kilometers per hour as t + 4 hours.
We know that time equals distance divided by speed. So, the ... | false | 204 | 37.7 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to first convert the time from hours and minutes to just minutes.
When Aya walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. Since 4 hours is equal to 240 minutes, we can write an equation:
240 + t = 9/s \* 60 (... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 46 | To solve this problem, we need to first convert the time from hours and minutes to just minutes.
When Aya walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. Since 4 hours is equal to 240 minutes, we can write an equation:
240 + t = 9/s \* 60 (... | false | 204 | 1082 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time it takes for Aya to walk 9 kilometers at speed $s$ kilometers per hour as $t_1$ hours, and the time it takes for her to walk 9 kilometers at speed $s + 2$ kilometers per hour as $t_2$ hours.
Given that th... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 47 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time it takes for Aya to walk 9 kilometers at speed $s$ kilometers per hour as $t_1$ hours, and the time it takes for her to walk 9 kilometers at speed $s + 2$ kilometers per hour as $t_2$ hours.
Given that th... | false | 204 | 240 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will break it down into steps.
## Step 1: Understand the problem
We are given information about Aya's walking speed and the time it takes her to walk 9 kilometers, including the time spent in a coffee shop. We need to find the total time it takes her to walk 9 kilometers at a speed of $s+\fra... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 48 | To solve this problem, we will break it down into steps.
## Step 1: Understand the problem
We are given information about Aya's walking speed and the time it takes her to walk 9 kilometers, including the time spent in a coffee shop. We need to find the total time it takes her to walk 9 kilometers at a speed of $s+\fra... | false | 204 | 927 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that the total time for the walk at the original speed $s$ is 4 hours, which includes $t$ minutes spent in... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 49 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that the total time for the walk at the original speed $s$ is 4 hours, which includes $t$ minutes spent in... | false | 204 | 240 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Set up the equation for the first scenario
When Aya walks at a speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. First, we convert 4 hours into minutes, which equals 240 minutes. We can set up ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 50 | To solve this problem, we'll break it down into steps.
## Step 1: Set up the equation for the first scenario
When Aya walks at a speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. First, we convert 4 hours into minutes, which equals 240 minutes. We can set up ... | false | 204 | 14300 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first express the time it takes Aya to walk 9 kilometers at different speeds. We will then create a system of linear equations to find the value of s.
## Step 1: Convert the time to hours and minutes
We are given that when Aya walks at a constant speed of s kilometers per hour, the walk ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 51 | To solve this problem, we will first express the time it takes Aya to walk 9 kilometers at different speeds. We will then create a system of linear equations to find the value of s.
## Step 1: Convert the time to hours and minutes
We are given that when Aya walks at a constant speed of s kilometers per hour, the walk ... | false | 204 | 3.4 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first convert all the time to hours and set up equations based on the information given.
Let's denote the time spent walking at $s$ km/h as $4 - \frac{t}{60}$ hours and the time spent walking at $s+2$ km/h as $2 + \frac{24}{60}$ hours.
We know that the distance covered in both cases is ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 52 | To solve this problem, we will first convert all the time to hours and set up equations based on the information given.
Let's denote the time spent walking at $s$ km/h as $4 - \frac{t}{60}$ hours and the time spent walking at $s+2$ km/h as $2 + \frac{24}{60}$ hours.
We know that the distance covered in both cases is ... | false | 204 | 216 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to follow a step-by-step approach.
## Step 1: Understand the problem and define variables
Let's denote the speed at which Aya walks as $s$ kilometers per hour, the time she spends walking as $t$ hours, and the distance of the walk as 9 kilometers. We need to find the total time taken for... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 53 | To solve this problem, we need to follow a step-by-step approach.
## Step 1: Understand the problem and define variables
Let's denote the speed at which Aya walks as $s$ kilometers per hour, the time she spends walking as $t$ hours, and the distance of the walk as 9 kilometers. We need to find the total time taken for... | false | 204 | 347 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to follow these steps:
## Step 1: Set up the equations for the two different walking speeds.
We know that time equals distance divided by speed. For the first scenario, the time taken is 4 hours, which is 240 minutes, and the speed is $s$ kilometers per hour. The time spent in the coffee... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 54 | To solve this problem, we need to follow these steps:
## Step 1: Set up the equations for the two different walking speeds.
We know that time equals distance divided by speed. For the first scenario, the time taken is 4 hours, which is 240 minutes, and the speed is $s$ kilometers per hour. The time spent in the coffee... | false | 204 | 199.23 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Define the given variables and the time it takes for Aya to walk 9 kilometers at different speeds.
Let's denote the speed of Aya's walk as $s$ kilometers per hour. The time it takes for her to walk 9 kilometers at this speed is given as 4 hours, includi... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 55 | To solve this problem, we'll break it down into steps.
## Step 1: Define the given variables and the time it takes for Aya to walk 9 kilometers at different speeds.
Let's denote the speed of Aya's walk as $s$ kilometers per hour. The time it takes for her to walk 9 kilometers at this speed is given as 4 hours, includi... | false | 204 | 886.7 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow a step-by-step approach.
## Step 1: Understand the problem
We have to find the time it takes Aya to walk 9 kilometers at a speed of $s + \frac{1}{2}$ kilometers per hour, including the time she spends in the coffee shop, which is denoted as $t$ minutes.
## Step 2: Define the vari... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 56 | To solve this problem, we will follow a step-by-step approach.
## Step 1: Understand the problem
We have to find the time it takes Aya to walk 9 kilometers at a speed of $s + \frac{1}{2}$ kilometers per hour, including the time she spends in the coffee shop, which is denoted as $t$ minutes.
## Step 2: Define the vari... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will break it down into steps.
## Step 1: Convert the time spent walking at s km/h to hours
We know that the time spent walking at s km/h is 4 hours. Since we also need to include t minutes spent in the coffee shop, we convert t minutes to hours. We have t minutes = t/60 hours.
## Step 2: Wr... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 57 | To solve this problem, we will break it down into steps.
## Step 1: Convert the time spent walking at s km/h to hours
We know that the time spent walking at s km/h is 4 hours. Since we also need to include t minutes spent in the coffee shop, we convert t minutes to hours. We have t minutes = t/60 hours.
## Step 2: Wr... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can use the concept of speed, time, and distance.
Let's start by using the formula: time = distance / speed.
When Aya walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. We can convert the time to hours by dividing by ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 58 | To solve this problem, we can use the concept of speed, time, and distance.
Let's start by using the formula: time = distance / speed.
When Aya walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. We can convert the time to hours by dividing by ... | false | 204 | 5.266 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will break it down into steps.
## Step 1: Understand the given information
Aya walks 9 kilometers and stops at a coffee shop afterwards. When she walks at a speed of s kilometers per hour, the total time taken is 4 hours, which includes t minutes spent in the coffee shop. When she walks at a ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 59 | To solve this problem, we will break it down into steps.
## Step 1: Understand the given information
Aya walks 9 kilometers and stops at a coffee shop afterwards. When she walks at a speed of s kilometers per hour, the total time taken is 4 hours, which includes t minutes spent in the coffee shop. When she walks at a ... | false | 204 | 293 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can follow these steps:
## Step 1: Convert the time spent walking at s kilometers per hour to just hours
We know that Aya walks at a constant speed of $s$ kilometers per hour. When she walks at this speed, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. We can conv... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 60 | To solve this problem, we can follow these steps:
## Step 1: Convert the time spent walking at s kilometers per hour to just hours
We know that Aya walks at a constant speed of $s$ kilometers per hour. When she walks at this speed, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. We can conv... | false | 204 | 1644 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time spent walking at speed $s$ kilometers per hour as $t$ hours, and the time spent walking at speed $s+2$ kilometers per hour as $t$ hours as well (since $t$ minutes is equivalent to $t/60$ hours).
We know t... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 61 | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time spent walking at speed $s$ kilometers per hour as $t$ hours, and the time spent walking at speed $s+2$ kilometers per hour as $t$ hours as well (since $t$ minutes is equivalent to $t/60$ hours).
We know t... | false | 204 | 214.29 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that the total time for the walk at $s$ kilometers per hour is 4 hours, and at $s+2$ kilometers per hour is... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 62 | To solve this problem, we'll start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that the total time for the walk at $s$ kilometers per hour is 4 hours, and at $s+2$ kilometers per hour is... | false | 204 | 14408 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to set up and solve a system of equations.
Let's start by converting the given times into just hours:
- When Aya walks at $s$ kilometers per hour, the total time is $4$ hours, which includes $t$ minutes spent in the coffee shop. We can express this as:
$$\frac{9}{s} + \frac{t}{60} = 4$$
... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 63 | To solve this problem, we need to set up and solve a system of equations.
Let's start by converting the given times into just hours:
- When Aya walks at $s$ kilometers per hour, the total time is $4$ hours, which includes $t$ minutes spent in the coffee shop. We can express this as:
$$\frac{9}{s} + \frac{t}{60} = 4$$
... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first convert all time to hours, since speed is in kilometers per hour.
## Step 1: Define the variables and the equation for the first scenario
Let's denote the time Aya spends walking as $w_1$ hours and the time she spends in the coffee shop as $t$ minutes, which is $\frac{t}{60}$ hours... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 64 | To solve this problem, we will first convert all time to hours, since speed is in kilometers per hour.
## Step 1: Define the variables and the equation for the first scenario
Let's denote the time Aya spends walking as $w_1$ hours and the time she spends in the coffee shop as $t$ minutes, which is $\frac{t}{60}$ hours... | false | 204 | 366 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first convert the given times into hours and set up equations based on the time it takes for Aya to walk 9 kilometers at different speeds.
Let's denote the time spent walking as $w$ hours. When Aya walks at $s$ kilometers per hour, the time spent walking is $\frac{9}{s}$ hours, and when ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 65 | To solve this problem, we will first convert the given times into hours and set up equations based on the time it takes for Aya to walk 9 kilometers at different speeds.
Let's denote the time spent walking as $w$ hours. When Aya walks at $s$ kilometers per hour, the time spent walking is $\frac{9}{s}$ hours, and when ... | false | 204 | 319 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that when she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 66 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as $w$ hours and the time she spends in the coffee shop as $t$ minutes. We know that when she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including ... | false | 204 | 180 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will first convert all times to hours and set up equations based on the given information.
Let's denote the time Aya spends walking at speed $s$ kilometers per hour as $t_s$ hours and the time she spends walking at speed $s+2$ kilometers per hour as $t_{s+2}$ hours.
We are given that when sh... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 67 | To solve this problem, we will first convert all times to hours and set up equations based on the given information.
Let's denote the time Aya spends walking at speed $s$ kilometers per hour as $t_s$ hours and the time she spends walking at speed $s+2$ kilometers per hour as $t_{s+2}$ hours.
We are given that when sh... | false | 204 | 12576 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Define the variables and understand the problem
Let's define the variables:
- $s$ = Aya's speed in kilometers per hour when she walks alone.
- $t$ = time spent in the coffee shop in minutes.
- The total time spent when walking at speed $s$ is 4 hours, w... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 68 | To solve this problem, we'll break it down into steps.
## Step 1: Define the variables and understand the problem
Let's define the variables:
- $s$ = Aya's speed in kilometers per hour when she walks alone.
- $t$ = time spent in the coffee shop in minutes.
- The total time spent when walking at speed $s$ is 4 hours, w... | false | 204 | 870000 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will start by setting up equations based on the information given in the problem.
Let's denote the time spent walking at the initial speed $s$ as $4 - \frac{t}{60}$ hours and the time spent walking at the speed $s+2$ as $2 - \frac{24}{60} = \frac{96}{60} - \frac{24}{60} = \frac{72}{60} = 1.2$... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 69 | To solve this problem, we will start by setting up equations based on the information given in the problem.
Let's denote the time spent walking at the initial speed $s$ as $4 - \frac{t}{60}$ hours and the time spent walking at the speed $s+2$ as $2 - \frac{24}{60} = \frac{96}{60} - \frac{24}{60} = \frac{72}{60} = 1.2$... | false | 204 | 91.18 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can use the concept of distance, speed, and time. Let's break down the problem step by step.
Let's denote the time Aya spends walking as $t_w$ hours and the time she spends in the coffee shop as $t_c$ hours.
We are given two scenarios:
1. When Aya walks at a constant speed of $s$ kilometers... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 70 | To solve this problem, we can use the concept of distance, speed, and time. Let's break down the problem step by step.
Let's denote the time Aya spends walking as $t_w$ hours and the time she spends in the coffee shop as $t_c$ hours.
We are given two scenarios:
1. When Aya walks at a constant speed of $s$ kilometers... | false | 204 | 210.3 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow these steps:
## Step 1: Convert the given times into just hours for both scenarios
When Aya walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. We can convert the time spent in the coffee shop to hours b... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 71 | To solve this problem, we will follow these steps:
## Step 1: Convert the given times into just hours for both scenarios
When Aya walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. We can convert the time spent in the coffee shop to hours b... | false | 204 | 2 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down step by step.
## Step 1: Convert given times to just hours for consistency
First, let's convert the given times into just hours for consistency. The first scenario takes 4 hours, and the second scenario takes 2 hours and 24 minutes, which is 2 + 24/60 = 2.4 hours.
## Step 2:... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 72 | To solve this problem, we'll break it down step by step.
## Step 1: Convert given times to just hours for consistency
First, let's convert the given times into just hours for consistency. The first scenario takes 4 hours, and the second scenario takes 2 hours and 24 minutes, which is 2 + 24/60 = 2.4 hours.
## Step 2:... | false | 204 | 120 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Define the variables and the equations
Let's denote the time Aya spends walking at $s$ kilometers per hour as $t_s$ hours and the time she spends walking at $s+2$ kilometers per hour as $t_{s+2}$ hours. The time spent in the coffee shop is $t$ minutes, ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 73 | To solve this problem, we'll break it down into steps.
## Step 1: Define the variables and the equations
Let's denote the time Aya spends walking at $s$ kilometers per hour as $t_s$ hours and the time she spends walking at $s+2$ kilometers per hour as $t_{s+2}$ hours. The time spent in the coffee shop is $t$ minutes, ... | false | 204 | 3.4 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Define the given information
- Aya walks 9 kilometers long at a speed of $s$ kilometers per hour.
- The total time taken, including the time spent in the coffee shop, is 4 hours when walking at $s$ kilometers per hour.
- The time spent in the coffee sho... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 74 | To solve this problem, we'll break it down into steps.
## Step 1: Define the given information
- Aya walks 9 kilometers long at a speed of $s$ kilometers per hour.
- The total time taken, including the time spent in the coffee shop, is 4 hours when walking at $s$ kilometers per hour.
- The time spent in the coffee sho... | false | 204 | 8471 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time Aya spends walking at a speed of $s$ kilometers per hour as $4 - \frac{t}{60}$ hours, and the time she spends walking at a speed of $s+2$ kilometers per hour as $2 + \frac{24}{60}$ hours.
Since distance =... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 75 | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time Aya spends walking at a speed of $s$ kilometers per hour as $4 - \frac{t}{60}$ hours, and the time she spends walking at a speed of $s+2$ kilometers per hour as $2 + \frac{24}{60}$ hours.
Since distance =... | false | 204 | \frac{2160}{11} |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to first determine the value of $t$ and then find the time it takes for Aya to walk at a speed of $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Understand the problem
We are given that Aya walks at a constant speed of $s$ kilometers per hour, taking 4 hours, including $t$ minutes spen... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 76 | To solve this problem, we need to first determine the value of $t$ and then find the time it takes for Aya to walk at a speed of $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Understand the problem
We are given that Aya walks at a constant speed of $s$ kilometers per hour, taking 4 hours, including $t$ minutes spen... | false | 204 | 102 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time Aya spends walking at $s$ kilometers per hour as $t_s$ and the time she spends walking at $s+2$ kilometers per hour as $t_{s+2}$. We know that the total time for each scenario includes $t$ minutes spent in... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 77 | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time Aya spends walking at $s$ kilometers per hour as $t_s$ and the time she spends walking at $s+2$ kilometers per hour as $t_{s+2}$. We know that the total time for each scenario includes $t$ minutes spent in... | false | 204 | 53 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow these steps:
## Step 1: First, we need to set up the equations based on the given information.
Let's denote the time spent walking at speed $s$ kilometers per hour as $t_s$ hours and the time spent walking at speed $s+2$ kilometers per hour as $t_{s+2}$ hours. We also denote the t... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 78 | To solve this problem, we will follow these steps:
## Step 1: First, we need to set up the equations based on the given information.
Let's denote the time spent walking at speed $s$ kilometers per hour as $t_s$ hours and the time spent walking at speed $s+2$ kilometers per hour as $t_{s+2}$ hours. We also denote the t... | false | 204 | 77 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will break it down into steps.
## Step 1: Define the variables
Let's define the variables: $s$ is Aya's constant walking speed in kilometers per hour, $t$ is the time spent in the coffee shop in minutes, and the total time for the walk is $T$.
## Step 2: Convert the total time from hours to ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 79 | To solve this problem, we will break it down into steps.
## Step 1: Define the variables
Let's define the variables: $s$ is Aya's constant walking speed in kilometers per hour, $t$ is the time spent in the coffee shop in minutes, and the total time for the walk is $T$.
## Step 2: Convert the total time from hours to ... | false | 204 | 247.2 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow these steps:
## Step 1: Convert the time from hours and minutes to just minutes
First, let's convert the time from hours and minutes to just minutes. The time it takes Aya to walk 9 kilometers at a speed of $s$ kilometers per hour is $\frac{9}{s}$ hours, which is equivalent to $\f... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 80 | To solve this problem, we will follow these steps:
## Step 1: Convert the time from hours and minutes to just minutes
First, let's convert the time from hours and minutes to just minutes. The time it takes Aya to walk 9 kilometers at a speed of $s$ kilometers per hour is $\frac{9}{s}$ hours, which is equivalent to $\f... | false | 204 | 2 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to find the value of $s$ and then use it to calculate the time taken for Aya's walk at $s+\frac{1}{2}$ kilometers per hour.
First, we'll convert the given times into hours. We have:
- Time taken at $s$ kilometers per hour: $4$ hours $= \frac{4}{60}$ hours $= \frac{1}{15}$ hours
- Time ta... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 81 | To solve this problem, we need to find the value of $s$ and then use it to calculate the time taken for Aya's walk at $s+\frac{1}{2}$ kilometers per hour.
First, we'll convert the given times into hours. We have:
- Time taken at $s$ kilometers per hour: $4$ hours $= \frac{4}{60}$ hours $= \frac{1}{15}$ hours
- Time ta... | false | 204 | 104 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Understand the given problem and define the variables.
Aya walks a 9-kilometer-long distance at two different speeds: $s$ kilometers per hour and $s+2$ kilometers per hour. The time spent walking and in the coffee shop is given for both speeds. We need ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 82 | To solve this problem, we'll break it down into steps.
## Step 1: Understand the given problem and define the variables.
Aya walks a 9-kilometer-long distance at two different speeds: $s$ kilometers per hour and $s+2$ kilometers per hour. The time spent walking and in the coffee shop is given for both speeds. We need ... | false | 204 | 223 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Define the given information and the variables involved.
Aya walks 9 kilometers. At a speed of $s$ km/h, the total time (including coffee shop time) is 4 hours, which is $240$ minutes. At a speed of $s+2$ km/h, the total time (including coffee shop time... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 83 | To solve this problem, we'll break it down into steps.
## Step 1: Define the given information and the variables involved.
Aya walks 9 kilometers. At a speed of $s$ km/h, the total time (including coffee shop time) is 4 hours, which is $240$ minutes. At a speed of $s+2$ km/h, the total time (including coffee shop time... | false | 204 | 1092\frac{2}{7} |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll break it down into steps.
## Step 1: Understand the problem
We are given that Aya walks a 9-kilometer-long distance. The time taken for the walk is different based on her walking speed. We need to find the time taken when she walks at a speed of $s+\frac{1}{2}$ kilometers per hour.
## Ste... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 84 | To solve this problem, we'll break it down into steps.
## Step 1: Understand the problem
We are given that Aya walks a 9-kilometer-long distance. The time taken for the walk is different based on her walking speed. We need to find the time taken when she walks at a speed of $s+\frac{1}{2}$ kilometers per hour.
## Ste... | false | 204 | 234 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to find the value of $t$ and then use it to calculate the time taken by Aya when she walks at $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Let's denote the time taken for the walk in hours as $w$. We know that $w + \frac{t}{60} = 4$ and $w + \frac{t}{60} = 2.4$.
## Step 2: Subtractin... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 85 | To solve this problem, we need to find the value of $t$ and then use it to calculate the time taken by Aya when she walks at $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Let's denote the time taken for the walk in hours as $w$. We know that $w + \frac{t}{60} = 4$ and $w + \frac{t}{60} = 2.4$.
## Step 2: Subtractin... | false | 204 | 232 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time Aya spends walking as $t_w$ and the time she spends in the coffee shop as $t_c$. We know that the total time for the walk is $4$ hours, which is equivalent to $240$ minutes, when walking at a speed of $s$ ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 86 | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time Aya spends walking as $t_w$ and the time she spends in the coffee shop as $t_c$. We know that the total time for the walk is $4$ hours, which is equivalent to $240$ minutes, when walking at a speed of $s$ ... | false | 204 | 240 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking at the normal speed $s$ kilometers per hour as $4-\frac{t}{60}$ hours, and the time she spends walking at the faster speed $s+2$ kilometers per hour as $2-\frac{24}{60}$ hours.
We can s... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 87 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking at the normal speed $s$ kilometers per hour as $4-\frac{t}{60}$ hours, and the time she spends walking at the faster speed $s+2$ kilometers per hour as $2-\frac{24}{60}$ hours.
We can s... | false | 204 | 4 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as \(W\) hours and the time she spends in the coffee shop as \(t\) minutes. We know that the total time for the walk at two different speeds is given.
1. When Aya walks at a constant sp... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 88 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking as \(W\) hours and the time she spends in the coffee shop as \(t\) minutes. We know that the total time for the walk at two different speeds is given.
1. When Aya walks at a constant sp... | false | 204 | 4 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to follow a step-by-step approach.
## Step 1: Define the variables
Let's define the variables: $s$ is Aya's walking speed in kilometers per hour, and $t$ is the time spent in the coffee shop in minutes.
## Step 2: Convert time to hours
Since the speeds are given in kilometers per hour, ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 89 | To solve this problem, we need to follow a step-by-step approach.
## Step 1: Define the variables
Let's define the variables: $s$ is Aya's walking speed in kilometers per hour, and $t$ is the time spent in the coffee shop in minutes.
## Step 2: Convert time to hours
Since the speeds are given in kilometers per hour, ... | false | 204 | 66 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to first find the value of $t$ and then use it to calculate the time it takes Aya to walk at $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Set up the equations for the two different walking speeds
Let's denote the time spent walking at speed $s$ kilometers per hour as $4-\frac{t}{60}$ ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 90 | To solve this problem, we need to first find the value of $t$ and then use it to calculate the time it takes Aya to walk at $s+\frac{1}{2}$ kilometers per hour.
## Step 1: Set up the equations for the two different walking speeds
Let's denote the time spent walking at speed $s$ kilometers per hour as $4-\frac{t}{60}$ ... | false | 204 | 702 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will break it down into steps.
## Step 1: Define the given information and the variables.
- Aya walks at a constant speed of $s$ kilometers per hour.
- The distance of the walk is 9 kilometers.
- When Aya walks at $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spen... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 91 | To solve this problem, we will break it down into steps.
## Step 1: Define the given information and the variables.
- Aya walks at a constant speed of $s$ kilometers per hour.
- The distance of the walk is 9 kilometers.
- When Aya walks at $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spen... | false | 204 | 402 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we'll first convert all the given times into hours and then establish equations based on the information provided.
Let's denote:
- $s$ as Aya's speed in kilometers per hour.
- $t$ as the time Aya spends in the coffee shop in minutes.
- The time Aya takes to walk 9 kilometers at speed $s$ as $t_{... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 92 | To solve this problem, we'll first convert all the given times into hours and then establish equations based on the information provided.
Let's denote:
- $s$ as Aya's speed in kilometers per hour.
- $t$ as the time Aya spends in the coffee shop in minutes.
- The time Aya takes to walk 9 kilometers at speed $s$ as $t_{... | false | 204 | 27 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to break it down into steps.
## Step 1: Set up the equation for the first scenario
We know that Aya walks at a constant speed of $s$ kilometers per hour. The total time it takes her to complete the 9-kilometer-long walk and stop at the coffee shop is 4 hours, including $t$ minutes spent ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 93 | To solve this problem, we need to break it down into steps.
## Step 1: Set up the equation for the first scenario
We know that Aya walks at a constant speed of $s$ kilometers per hour. The total time it takes her to complete the 9-kilometer-long walk and stop at the coffee shop is 4 hours, including $t$ minutes spent ... | true | 204 | 204 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, let's break it down step by step.
## Step 1: Convert time to hours
First, let's convert the given times to hours for easier calculation. We have two scenarios:
- When Aya walks at speed $s$ km/h, the walk takes 4 hours, including $t$ minutes spent in the coffee shop. We need to convert $t$ minut... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 94 | To solve this problem, let's break it down step by step.
## Step 1: Convert time to hours
First, let's convert the given times to hours for easier calculation. We have two scenarios:
- When Aya walks at speed $s$ km/h, the walk takes 4 hours, including $t$ minutes spent in the coffee shop. We need to convert $t$ minut... | false | 204 | 552 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow a step-by-step approach.
## Step 1: Define the variables and the equations
Let $s$ be Aya's constant speed in kilometers per hour. The time it takes her to walk 9 kilometers at speed $s$ is $\frac{9}{s}$ hours, and the time spent in the coffee shop is $t$ minutes, which is $\frac{... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 95 | To solve this problem, we will follow a step-by-step approach.
## Step 1: Define the variables and the equations
Let $s$ be Aya's constant speed in kilometers per hour. The time it takes her to walk 9 kilometers at speed $s$ is $\frac{9}{s}$ hours, and the time spent in the coffee shop is $t$ minutes, which is $\frac{... | false | 204 | 196 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking at the initial speed $s$ kilometers per hour as $4 - \frac{t}{60}$ hours, and the time she spends walking at the speed $s+2$ kilometers per hour as $2 - \frac{24}{60}$ hours.
The dista... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 96 | To solve this problem, we can start by setting up equations based on the information given.
Let's denote the time Aya spends walking at the initial speed $s$ kilometers per hour as $4 - \frac{t}{60}$ hours, and the time she spends walking at the speed $s+2$ kilometers per hour as $2 - \frac{24}{60}$ hours.
The dista... | false | 204 | 714 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we need to first convert the time taken for each scenario into hours.
Let's denote the time taken for the walk at speed s kilometers per hour as $t_{walk,s}$ and the time taken for the walk at speed $s+2$ kilometers per hour as $t_{walk,s+2}$. We are also given that $t$ is the time spent in the ... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 97 | To solve this problem, we need to first convert the time taken for each scenario into hours.
Let's denote the time taken for the walk at speed s kilometers per hour as $t_{walk,s}$ and the time taken for the walk at speed $s+2$ kilometers per hour as $t_{walk,s+2}$. We are also given that $t$ is the time spent in the ... | false | 204 | 196.2 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we will follow these steps:
## Step 1: First, let's establish the variables and the given information.
- Let $s$ be Aya's walking speed in kilometers per hour.
- Let $t$ be the time spent in the coffee shop in minutes.
- We are given that the total time for the walk at speed $s$ is 4 hours, inc... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 98 | To solve this problem, we will follow these steps:
## Step 1: First, let's establish the variables and the given information.
- Let $s$ be Aya's walking speed in kilometers per hour.
- Let $t$ be the time spent in the coffee shop in minutes.
- We are given that the total time for the walk at speed $s$ is 4 hours, inc... | false | 204 | 221 |
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks... | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time spent walking at the original speed $s$ as $4-\frac{t}{60}$ hours (since $t$ minutes is equivalent to $\frac{t}{60}$ hours), and the time spent walking at the increased speed $s+2$ as $2-\frac{24}{60}$ hou... | Every morning Aya goes for a $9$-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of $s$ kilometers per hour, the walk takes her 4 hours, including $t$ minutes spent in the coffee shop. When she walks $s+2$ kilometers per hour, the walk takes her 2 hours and 24 minutes, incl... | 204 | 0 | 99 | To solve this problem, we can start by setting up equations based on the given information.
Let's denote the time spent walking at the original speed $s$ as $4-\frac{t}{60}$ hours (since $t$ minutes is equivalent to $\frac{t}{60}$ hours), and the time spent walking at the increased speed $s+2$ as $2-\frac{24}{60}$ hou... | false | 204 | 5409 |
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