Multiple choice

The distance between two spots A & B, on the same bank of the river ,is $75 km$. Speed of the boat in still water is twice as much as that of the speed of the water current of the river. The boat travels in the river from $A$ to $B$ and returns back to the spot in $16 hour$. What is the speed of the boat in still water?

  1. $12.5 kmph$
  2. $15 kmph$
  3. $16 kmph$
  4. $18 kmph$
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A Correct answer
Explanation

Let current = x, boat = 2x. Downstream = 3x, Upstream = x. 75/(3x) + 75/x = 16. 25/x + 75/x = 16. 100/x = 16. x = 6.25. Boat speed = 2x = 12.5.

AI explanation

Let the speed of the water current be x, making the boat's speed in still water 2x. The downstream speed is 3x and the upstream speed is x, giving an average speed for the round trip of (2 * 3x * x) / (3x + x) = 1.5x. The total time for the 75 km round trip is 150 / 1.5x = 16 hours, which yields an x value of 6.25 kmph; therefore, the speed of the boat in still water (2x) is 12.5 kmph.

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