Multiple choice

A boat takes 11 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream be 3 km/hr and the speed of the boat in still water be `12 km/hr, then what is the distance between A and B ?

  1. $100$ km
  2. $90$ km
  3. $110$ km
  4. $120$ km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance AB = D. Downstream speed = 12+3 = 15 km/hr. Upstream speed = 12-3 = 9 km/hr. Time = D/15 + (D/2)/9 = 11. D/15 + D/18 = 11. (6D + 5D)/90 = 11. 11D/90 = 11. D = 90 km.

AI explanation

Let the distance between A and B be D km; the speed downstream is 12 plus 3 equals 15 km/hr, and the speed upstream is 12 minus 3 equals 9 km/hr. The total time for travelling from A to B and returning to C midway is D divided by 15 plus D divided by 2 and then divided by 9, which equals 11 hours. Solving the equation D divided by 15 plus D divided by 18 equals 11 gives 11D divided by 90 equals 11, so D equals 90 km.

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