Multiple choice

A man takes half time in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?

  1. 1 : 2

  2. 2 : 1

  3. 1 : 3

  4. 3 : 1
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D Correct answer
Explanation

Let speed in still water be x and speed of current be y. Downstream speed = x+y, upstream speed = x-y. Time = Distance/Speed. Given 1/(x+y) = 1/2 * 1/(x-y), so 2(x-y) = x+y. 2x - 2y = x + y, which simplifies to x = 3y. The ratio x:y is 3:1.

AI explanation

Because the downstream distance is covered in half the time of the upstream distance, the downstream speed must be twice the upstream speed. Using the boat and stream formulas, this gives (x plus y) equals 2 multiplied by (x minus y), which simplifies to 3y equals x. The ratio of the speed in still water to the speed of the current is 3 : 1.

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