To find the speed of a river's current, boatman decides to carry out the following experiment. He drops a wooden bucket into the water and himself sets off downstream, rowing along the flow of river. After 40 min, he reaches a point A, 1km from his starting-point and turns back. After travelling some distance upstream, he picks up the bucket, turns round again and, rowing downstram once more, reaches A for the second time 24 min later (after picking the bucket). Assuming that the speeds of both current and boat (w.r.t. river) are constant, and also that no time is wasted on turning round. What is the boat's speed relative to the water?

Options

A. `1.2 km//hr`
B. `1 km//hr`
C. `0.75 km//hr`
D. None of these

Answer

A

Explanation

Relative to the bucket (which floats downstream) the boat's speed upstream and downstream must be the same. Thus the boatman also spends 40 min on returning to meet the bucket. Further, the speed of the boat downstream relative to the bank is `25m//min` (since it takes 40 min to travel 1km to point A). After meeting the bucket, the boat spends 24min on returning downstram, so the meeting place is 600 m before A, or 400 m from the place where the bucket is lowered into the water. Thus the bucket travels 400 m in the 80 min between being lowered and pickup up, i.e. the speed of the current is `5m//min` and that of the boat relative to the water is `20m//min`.