MCES10/maths-problems-gemma-2-2b-it-GGUF

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

Based on OpenR1-Math-220k

Input:

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.

Output:

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.

========== Prompt: 114 tokens, 417.293 tokens-per-sec Generation: 358 tokens, 28.375 tokens-per-sec Peak memory: 5.406 GB