---
license: apache-2.0
datasets:
- open-r1/OpenR1-Math-220k
language:
- en
pipeline_tag: text-generation
---

# Maths Problem Solving AI Based on Google Gemma 2 2b it GGUF


## 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