Question

A man can swim with a speed of 3 m/s in still water. He crosses a river of width 100 m by swimming in the direction that will take him across in the smallest possible time. When he reaches the opposite shore, he has been swept 50 m downstream. How fast is the river flowing?

Answer 1

Explanation:

The given data is as follows.

           width = 100 m,          speed = 3 m/s

So, minimum time required to cross the stream is calculated as follows.

          t = $\frac{100 m}{3 m/s}$          

Also, in the  same time the man has moved downstream by 50 meter.

Hence, distance traveled downstream is as follows.

            d = velocity of river × t

        $v_{river} = \frac{d}{t}$

                   = $\frac{50}{\frac{100}{3}}$

                   = $\frac{3}{2}$

                   = 1.5 m/s

Thus, we can conclude that the river is flowing by 1.5 m/s.