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A boat travels 24 km upstream and 28 km downstream in 9 hours. It also travels 30 km upstream and 21 km downstream in 10 hours. Find the speed of the boat in still water.

1. 6.50 km/h
2. 7.45 km/h
3. 10.45 km/h
4. 12 km/h

Correct answer: 7.45 km/h

Solution

Let the speed of the boat in still water be $b$ km/h and the speed of the stream be $s$ km/h. Then $\frac{24}{b-s}+\frac{28}{b+s}=9$ and $\frac{30}{b-s}+\frac{21}{b+s}=10$. Solving these simultaneous equations gives $b=7.45$ km/h.

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