Multiple choice

Find the speed of flow of water in a stream if a motorboat takes exactly 90 minutes less to travel a distance of 36 miles downstream than to travel the exact same distance upstream. [Note: Speed of the boat in still water is 10 mph]

  1. 2 mph

  2. 3 mph

  3. 4 mph

  4. 5 mph

  5. 6 mph
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A Correct answer
Explanation

Let v be the stream speed. Downstream speed is 10+v, upstream is 10-v. Time difference: 36/(10-v) - 36/(10+v) = 1.5 hours. Solving 36(10+v) - 36(10-v) = 1.5(100-v^2) leads to 72v = 150 - 1.5v^2, or v^2 + 48v - 100 = 0. Factoring gives (v+50)(v-2) = 0, so v = 2.

AI explanation

Let the stream speed be x, so the upstream and downstream speeds are 10 - x and 10 + x respectively. The 90-minute time difference means 36 / (10 - x) - 36 / (10 + x) = 1.5, which simplifies to x^2 = 4, giving x = 2. The result is 2 mph.

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