A man swimming in a stream which flows 1\(\frac{1}{2}\) km/hr, he finds that in a given time he can swim twice as far with the stream as he can against it. Find speed of boat in still water.

4\(\frac{1}{2}\)

If time is constant, then ratio of speed = ratio of distance

ATQ,

        Downstream (D.S)     :     Upstream (U.S)

Distance        2                   :                1

Speed            2                  :                1

Speed of boat in still water (u) = \(\frac{D.S.\;+\;U.S.}{2}\) = \(\frac{2\;+\;1}{2}\) = \(\frac{3}{2}\)

Speed of stream (v)= \(\frac{D.S.\;-\;U.S.}{2}\) = \(\frac{2\;+\;1}{2}\) = \(\frac{1}{2}\)

⇒  u : v = \(\frac{3}{2}\) : \(\frac{1}{2}\) = 3 : 1

1R =  1\(\frac{1}{2}\) = \(\frac{3}{2}\) (given)

3R = \(\frac{9}{2}\) = 4\(\frac{1}{2}\)