Multiple choice

A man rows to a place and back in 12 hours, covering a distance of 45 km. He realises that he can row 5 km downstream in the same time as 3 km against the stream. The velocity of the stream is

  1. 2 km/hr

  2. 1.5 km/hr

  3. 1 km/hr

  4. 4 km/hr
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A Correct answer
Explanation

Let u be boat speed, v be stream speed. Downstream = u+v, upstream = u-v. 5/(u+v) = 3/(u-v) => 5u - 5v = 3u + 3v => 2u = 8v => u = 4v. Total time = 45/(u+v) + 45/(u-v) = 12. 45/(5v) + 45/(3v) = 12. 9/v + 15/v = 12. 24/v = 12. v = 2.

AI explanation

Since he rows 5 km downstream in the same time he rows 3 km upstream, the ratio of his downstream speed to his upstream speed is 5 to 3. Let the downstream and upstream speeds be 5x and 3x; his total time for the 45 km round trip is 22.5 divided by 5x plus 22.5 divided by 3x, which equals 12. Solving 1.5 divided by x plus 4.5 divided by x equals 12 yields x equals 0.5. The stream velocity is half the difference of the downstream and upstream speeds, so 0.5 times (2.5 minus 1.5) equals 2 km/hr.

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