Multiple choice

The ratio of the speed of boat in still water to the speed of stream is 13 : 7. A boat goes 24 km upstream in 60 minutes. Find the time taken by the boat to cover the distance of 21 km downstream.

  1. 15 minutes 45 seconds

  2. 16 minutes 10 seconds

  3. 18 minutes 25 seconds

  4. 20 minutes 20 seconds

  5. 22 minutes 40 seconds
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A Correct answer
Explanation

Speed ratio (boat:stream) = 13:7. Let speeds be 13x and 7x. Upstream speed = 13x - 7x = 6x. 24 km in 60 min (1 hr) means speed = 24 km/h. So 6x = 24, x = 4. Boat speed = 52 km/h, stream speed = 28 km/h. Downstream speed = 52 + 28 = 80 km/h. Time for 21 km = 21/80 hours = (21/80) * 60 minutes = 21 * 0.75 = 15.75 minutes. 0.75 minutes = 45 seconds. Total time = 15 minutes 45 seconds.

AI explanation

Given the ratio of the speed of the boat in still water to the speed of the stream is 13:7, the upstream speed is 13x minus 7x, giving 6x. Since the boat goes 24 km upstream in 60 minutes, 6x equals 24, so x equals 4 kmph. The downstream speed is 13x plus 7x, giving 20x, which calculates to 80 kmph. Using the Time formula, the time to cover 21 km downstream is 21 divided by 80 hours, which equals 0.2625 hours; converting this by multiplying by 3600 gives 945 seconds. This time is equal to 15 minutes and 45 seconds.

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