Multiple choice

A motor boat covers a given distance in $6\ h$ moving downstream of a river. It covers the same distance in $10\ h$ moving upstream. The time (in hour) it takes to cover the same distance in still water is

  1. $6\ h$
  2. $7.5\ h$
  3. $10\ h$
  4. $15\ h$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be boat speed, u be stream speed. Downstream: v+u = D/6. Upstream: v-u = D/10. Adding: 2v = D/6 + D/10 = (5D+3D)/30 = 8D/30 = 4D/15. v = 2D/15. Time in still water = D/v = D / (2D/15) = 15/2 = 7.5 hours.

AI explanation

Let the distance be D, the speed of the boat in still water be v, and the speed of the stream be u. The downstream speed (v plus u) equals D/6, and the upstream speed (v minus u) equals D/10; adding these two equations gives twice the boat's speed in still water, so 2v equals D times the sum of 1/6 and 1/10, which is 4D/15. Dividing by 2 gives v equals 2D/15, and the time taken to cover the distance D in still water is D divided by (2D/15). The time is 15/2 hours, which equals 7.5 hours.

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