Multiple choice

A man can row against the current three-fourth of a kilometre in 15 minutes and returns the same distance in 10 minutes. The ratio of his speed to that of the current is

  1. 3 : 5

  2. 5 : 3

  3. 1 : 5

  4. 5 : 1
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D Correct answer
Explanation

Speed against current (u-v) = (3/4 km) / (15/60 h) = 3 km/h. Speed with current (u+v) = (3/4 km) / (10/60 h) = 4.5 km/h. Solving u-v=3 and u+v=4.5 gives 2u=7.5 (u=3.75) and 2v=1.5 (v=0.75). Ratio u:v = 3.75:0.75 = 5:1.

AI explanation

The upstream speed is 0.75 km divided by (15 divided by 60) hours, which equals 3 km/h, and the downstream speed is 0.75 km divided by (10 divided by 60) hours, which equals 4.5 km/h. The man's rowing speed in still water is the average of these two speeds, giving (3 plus 4.5) divided by 2 to equal 3.75 km/h. The speed of the current is half the difference of the downstream and upstream speeds, resulting in (4.5 minus 3) divided by 2 to equal 0.75 km/h. The ratio of the man's speed to the current's speed is 3.75 divided by 0.75, which simplifies to 5:1.

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