A man can row at a speed of 15 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 9 km/hr. Find his average speed for total journey.a.8.4 km/hrb.9.6 km/hrc.9.1 km/hrd.10.4 km/hr
Question
A man can row at a speed of 15 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 9 km/hr. Find his average speed for total journey.a.8.4 km/hrb.9.6 km/hrc.9.1 km/hrd.10.4 km/hr
Solution
The man's speed in still water (v) is 15 km/hr and the speed of the stream (u) is 9 km/hr.
When the man is rowing upstream (against the current), his effective speed is (v - u) = (15 - 9) = 6 km/hr.
When he is rowing downstream (with the current), his effective speed is (v + u) = (15 + 9) = 24 km/hr.
The average speed is given by the total distance travelled divided by the total time taken.
The total distance travelled is twice the distance to the upstream point (once going upstream and once coming downstream). Let's call this distance 'd'. So, the total distance = 2d.
The time taken to travel upstream = d/(v - u) = d/6 hours. The time taken to travel downstream = d/(v + u) = d/24 hours.
So, the total time = d/6 + d/24 = (4d + d)/24 = 5d/24 hours.
Therefore, the average speed = total distance / total time = 2d / (5d/24) = (2 * 24) / 5 = 9.6 km/hr.
So, the answer is (b) 9.6 km/hr.
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