Multiple choice

A boatman rows to a place 45 km distant and back in 20 hours. He finds that he can row 12 km with the stream in the same time as 4 km against the stream. Find the speed of the stream.

  1. 3 km/hr

  2. 2.5 km/hr

  3. 4 km/hr

  4. Cannot be determined
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A Correct answer
Explanation

Let boat speed be u and stream speed be v. 12/(u+v) = 4/(u-v) => 12u - 12v = 4u + 4v => 8u = 16v => u = 2v. Total time = 45/(u+v) + 45/(u-v) = 20. 45/(3v) + 45/v = 20 => 15/v + 45/v = 20 => 60/v = 20 => v = 3 km/hr.

AI explanation

Let the boat's speed in still water be u km/hr and the stream's speed be v km/hr. The time to row 12 km downstream equals the time to row 4 km upstream, giving the equation 12 / (u + v) = 4 / (u - v), which simplifies to 2u = 4v or u = 2v. The total time for the 45 km trip is 20 hours, so 45 / (u + v) + 45 / (u - v) = 20. Substituting u = 2v gives 45 / 3v + 45 / v = 20, which simplifies to 60 / v = 20, meaning v = 3. The speed of the stream is 3 km/hr.

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