A boat's out-and-back run takes 4 hours when the current is 2 km/h. When the current doubles to 4 km/h, the same run takes 5 hours. What is the boat's speed in still water?

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Accepted Answer

8 km/h. Round-trip time ∝ b/(b² − s²), so 4/5 = (b² − 16)/(b² − 4) ⇒ 4b² − 16 = 5b² − 80 ⇒ b² = 64 ⇒ b = 8 km/h. (Each way is then 15 km.)

A boat's out-and-back run takes 4 hours when the current is 2 km/h. When the current doubles to 4 km/h, the same run takes 5 hours. What is the boat's speed in still water?

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