Multiple choice

A motor boat covers the distance between two places on a river and returns in $14 \ hrs$. If the velocity of the boat in still water is $35 \ km/h$ and velocity of water in the river is $5 \ km/h$, then the distance between the two places is

  1. $100 \ km$
  2. $240 \ km$
  3. $220\  km$
  4. $180\  km$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let d be the distance. Speed downstream = 35 + 5 = 40 km/h. Speed upstream = 35 - 5 = 30 km/h. Time = d/40 + d/30 = 14. (3d + 4d) / 120 = 14. 7d / 120 = 14. d = 240 km.

AI explanation

Let the distance between the two places be D. The downstream speed is 35 plus 5, giving 40 km/h, and the upstream speed is 35 minus 5, giving 30 km/h. The total time for the round trip is the sum of the downstream and upstream times, so D divided by 40 plus D divided by 30 equals 14 hours. Finding a common denominator gives 3D plus 4D divided by 120 equals 14, which simplifies to 7D divided by 120 equals 14, yielding D equals 240 km.

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