Multiple choice

A man rows 54 km downstream in 6 hours and 35 km upstream in 7 hours. Find the time taken by the man to row 48 km upstream, if speed of the boat in still water is increased by 14.28%.

  1. 6 hours

  2. 4 hours

  3. 8 hours

  4. 11 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Downstream speed = 54/6 = 9 km/hr. Upstream speed = 35/7 = 5 km/hr. Boat speed = (9+5)/2 = 7 km/hr. Stream speed = (9-5)/2 = 2 km/hr. New boat speed = 7 * 1.1428 = 8 km/hr. New upstream speed = 8 - 2 = 6 km/hr. Time for 48 km = 48/6 = 8 hours.

AI explanation

The initial upstream speed is 35 km divided by 7 hours, which equals 5 km/h. Because a 14.28% increase equals a multiplier of 1/7, the new speed of the boat in still water is calculated by adding the stream speed to find the original still water speed, but we only need the new upstream speed. The new upstream speed is 5 km/h multiplied by (8/7), giving approximately 5.71 km/h, which makes the time for 48 km roughly 8.4 hours. The stream speed is found by taking the downstream speed of 9 km/h and subtracting the 5 km/h upstream speed, then dividing by 2 to get 2 km/h, meaning the original boat speed was 7 km/h. Increasing 7 km/h by 14.28% gives a new boat speed of 8 km/h, so the new upstream speed is 6 km/h, and 48 km divided by 6 km/h equals 8 hours. The result is 8 hours.

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