Multiple choice

A swimmer swims from a point A against a current for 10 minutes before he reaches point C and then swims back along the current for next 10 minutes and comes to point B. If the distance between A and B is 200 metres, find the speed of the current (in kmph) :

  1. 0.6

  2. 0.5

  3. 0.4

  4. 0.9
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A Correct answer
Explanation

Let v be swimmer speed and c be current speed. Distance A to C = (v-c) * (10/60). Distance C to B = (v+c) * (10/60). A to B = AC - CB = (v-c)/6 - (v+c)/6 = -2c/6 = -c/3. The magnitude is 200m = 0.2km. So c/3 = 0.2, c = 0.6 kmph.

AI explanation

Let the swimmer's speed in still water be u and the speed of the current be v, making the upstream speed u - v and the downstream speed u + v. Swimming upstream for 10 minutes (which is 1/6 of an hour) places him at point C, so the distance AC is (u - v) / 6. Swimming downstream for 10 minutes places him at point B, so the distance from A to B is the downstream distance minus the upstream distance, calculated as (u + v) / 6 minus (u - v) / 6 equals 2v / 6 equals v / 3. Setting this equal to the 200 metres (0.2 km) between A and B gives v / 3 equals 0.2, so v equals 0.6 kmph.

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