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.
Answer & explanation
Correct answer: option 1
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\(\frac{1}{2}\)