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The speed of a boat in still water is $3x$ km/h, and the speed of the stream is $x$ km/h. If \[ \frac{24}{3x+x}+\frac{24}{3x-x}=6, \] find the value of $x$.

1. 2 km/hr
2. 3 km/hr
3. 4 km/hr
4. 5 km/hr

Correct answer: 3 km/hr

Solution

The upstream speed is $3x-x=2x$ and the downstream speed is $3x+x=4x$. Substituting gives $\frac{24}{4x}+\frac{24}{2x}=6$, which simplifies to $\frac{6}{x}+\frac{12}{x}=6$ and hence $x=3$.

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