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---
license: cc-by-3.0
datasets:
- open-r1/OpenR1-Math-220k
language:
- en
pipeline_tag: text-generation
---
# Maths Problem Solving AI Based on Google Gemma 2 2b it
## Based on OpenR1-Math-220k
Input:
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A ship traveling along a river has covered $24 \mathrm{~km}$ upstream and $28 \mathrm{~km}$ downstream. For this journey, it took half an hour less than for traveling $30 \mathrm{~km}$ upstream and $21 \mathrm{~km}$ downstream, or half an hour more than for traveling $15 \mathrm{~km}$ upstream and $42 \mathrm{~km}$ downstream, assuming that both the ship and the river move uniformly. Determine the speed of the ship in still water and the speed of the river.
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Output:
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Here's how to solve this problem:
**Let's denote:**
* *x* = speed of the ship in still water
* *y* = speed of the river
**Formulate the equations:**
* **Upstream:** *x - y* = *x* / 2 (The ship travels against the current, so its speed is reduced)
* **Downstream:** *x + y* = *x* / 2 (The ship travels with the current, so its speed is increased)
**Solve the system of equations:**
1. **Simplify the equations:**
* *x - y = x/2* => *x - x/2 = y* => *x/2 = y*
* *x + y = x/2* => *x + x/2 = y* => *3x/2 = y*
2. **Substitute the value of *y* from the first equation into the second equation:**
* *x/2 = 3x/2*
3. **Solve for *x*:**
* *x = 0*
4. **Substitute the value of *x* back into the equation for *y*:**
* *y = 0*
**Answer:**
* The speed of the ship in still water is 0 km/h.
* The speed of the river is 0 km/h.
**Conclusion:**
The ship is stationary, and the river is also stationary. This means that the ship and the river are at rest relative to each other.
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Prompt: 114 tokens, 417.293 tokens-per-sec
Generation: 358 tokens, 28.375 tokens-per-sec
Peak memory: 5.406 GB |