Multiple choice

The crew of a boat can row at the rate of 5 mph in still water. To row 24 miles against the stream, they take 4 times as long as to row the same distance down the river. Find the speed at which the river flows.

  1. 2 mph

  2. 2.5 mph

  3. 3 mph

  4. 3.5 mph

  5. 4 mph
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C Correct answer
Explanation

Let v be the speed of the stream. Speed downstream = 5 + v, speed upstream = 5 - v. Time = Distance / Speed. 24 / (5 - v) = 4 * (24 / (5 + v)). Simplifying gives 5 + v = 4(5 - v), so 5 + v = 20 - 4v, 5v = 15, v = 3 mph.

AI explanation

Let the speed of the river be r. The upstream speed is 5 - r and the downstream speed is 5 + r. Since the time taken to row 24 miles upstream is 4 times the time taken to row downstream, 24 / (5 - r) equals 4 times 24 / (5 + r). Simplifying this equation gives 5 + r = 20 - 4r, so 5r = 15 and r = 3 mph.

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