Question

A swimmer swims 3/5 the width of a river at one velocity, then swims the remainder of the river at half her initial velocity. What was the average speed across the river?

Answer 1

Let her initial velocity be U.

Let the width of the river be W.

She swims 3/5 the width of the river at U.

Remainder width = (1 - 3/5) = 2/5.

She then swims 2/5 the width with velocity U/2.


Average Speed = (Total Distance Traveled) / ( Total Time Taken).


Distance = Speed * time

time = Distance / Speed.

Time in first trip: = (3/5)W / U = 0.6W/U.

Time in second trip = (2/5)W / (U/2) = 0.4W / 0.5 U = 0.8W/U

Total Distance Traveled = W, width of the river.

Average Speed = W / (0.6W/U + 0.8W/U) = W / (1.4W/U)

= W * U / 1.4W
= U/1.4
= U * 10 / 14
= (5/7) U.

Therefore Average speed is (5/7) of the initial speed.