Update README.md
Browse files
README.md
CHANGED
|
@@ -1,3 +1,62 @@
|
|
| 1 |
-
---
|
| 2 |
-
license: cc-by-3.0
|
| 3 |
-
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
---
|
| 2 |
+
license: cc-by-3.0
|
| 3 |
+
datasets:
|
| 4 |
+
- open-r1/OpenR1-Math-220k
|
| 5 |
+
language:
|
| 6 |
+
- en
|
| 7 |
+
pipeline_tag: text-generation
|
| 8 |
+
---
|
| 9 |
+
|
| 10 |
+
# Maths Problem Solving AI Based on Google Gemma 2 2b it
|
| 11 |
+
|
| 12 |
+
|
| 13 |
+
## Based on OpenR1-Math-220k
|
| 14 |
+
|
| 15 |
+
|
| 16 |
+
Input:
|
| 17 |
+
==========
|
| 18 |
+
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.
|
| 19 |
+
==========
|
| 20 |
+
|
| 21 |
+
Output:
|
| 22 |
+
==========
|
| 23 |
+
Here's how to solve this problem:
|
| 24 |
+
|
| 25 |
+
**Let's denote:**
|
| 26 |
+
|
| 27 |
+
* *x* = speed of the ship in still water
|
| 28 |
+
* *y* = speed of the river
|
| 29 |
+
|
| 30 |
+
**Formulate the equations:**
|
| 31 |
+
|
| 32 |
+
* **Upstream:** *x - y* = *x* / 2 (The ship travels against the current, so its speed is reduced)
|
| 33 |
+
* **Downstream:** *x + y* = *x* / 2 (The ship travels with the current, so its speed is increased)
|
| 34 |
+
|
| 35 |
+
**Solve the system of equations:**
|
| 36 |
+
|
| 37 |
+
1. **Simplify the equations:**
|
| 38 |
+
* *x - y = x/2* => *x - x/2 = y* => *x/2 = y*
|
| 39 |
+
* *x + y = x/2* => *x + x/2 = y* => *3x/2 = y*
|
| 40 |
+
|
| 41 |
+
2. **Substitute the value of *y* from the first equation into the second equation:**
|
| 42 |
+
* *x/2 = 3x/2*
|
| 43 |
+
|
| 44 |
+
3. **Solve for *x*:**
|
| 45 |
+
* *x = 0*
|
| 46 |
+
|
| 47 |
+
4. **Substitute the value of *x* back into the equation for *y*:**
|
| 48 |
+
* *y = 0*
|
| 49 |
+
|
| 50 |
+
**Answer:**
|
| 51 |
+
|
| 52 |
+
* The speed of the ship in still water is 0 km/h.
|
| 53 |
+
* The speed of the river is 0 km/h.
|
| 54 |
+
|
| 55 |
+
**Conclusion:**
|
| 56 |
+
|
| 57 |
+
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.
|
| 58 |
+
|
| 59 |
+
==========
|
| 60 |
+
Prompt: 114 tokens, 417.293 tokens-per-sec
|
| 61 |
+
Generation: 358 tokens, 28.375 tokens-per-sec
|
| 62 |
+
Peak memory: 5.406 GB
|