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- ---
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- license: apache-2.0
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- ---
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ ---
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+ license: apache-2.0
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+ datasets:
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+ - open-r1/OpenR1-Math-220k
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+ language:
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+ - en
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+ pipeline_tag: text-generation
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+ ---
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+
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+ # Maths Problem Solving AI Based on Google Gemma 2 2b it GGUF
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+
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+
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+ ## Based on OpenR1-Math-220k
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+
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+
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+ Input:
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+ ==========
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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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+ ==========
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+
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+ Output:
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+ ==========
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+ Here's how to solve this problem:
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+
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+ **Let's denote:**
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+
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+ * *x* = speed of the ship in still water
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+ * *y* = speed of the river
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+
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+ **Formulate the equations:**
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+
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+ * **Upstream:** *x - y* = *x* / 2 (The ship travels against the current, so its speed is reduced)
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+ * **Downstream:** *x + y* = *x* / 2 (The ship travels with the current, so its speed is increased)
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+
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+ **Solve the system of equations:**
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+
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+ 1. **Simplify the equations:**
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+ * *x - y = x/2* => *x - x/2 = y* => *x/2 = y*
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+ * *x + y = x/2* => *x + x/2 = y* => *3x/2 = y*
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+
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+ 2. **Substitute the value of *y* from the first equation into the second equation:**
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+ * *x/2 = 3x/2*
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+
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+ 3. **Solve for *x*:**
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+ * *x = 0*
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+
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+ 4. **Substitute the value of *x* back into the equation for *y*:**
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+ * *y = 0*
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+
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+ **Answer:**
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+
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+ * The speed of the ship in still water is 0 km/h.
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+ * The speed of the river is 0 km/h.
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+
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+ **Conclusion:**
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+
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+ 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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+
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+ ==========
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+ Prompt: 114 tokens, 417.293 tokens-per-sec
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+ Generation: 358 tokens, 28.375 tokens-per-sec
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+ Peak memory: 5.406 GB