A motorboat covers a given distance in 6 hr moving downstream on a river.

A motorboat covers a given distance in 6 hr moving downstream on a river. It covers the same distance in 10 hr moving upstream. The time it takes to cover the same distance in still water is

1) 9 hr

2) 7.5 hr

3) 6.5 hr

4) 8 hr

Answer: 2) 7.5 hr

Solution:

 velocity of water = vw 

velocity of motorboat in still water. = vb

 The distance covered by motorboat in moving downstream in 6h 

 x=(vb+vw)×6…(1)

 The same distance covered by motorboat in moving upstream in 10h is

 x=(vb−vw)×10…(2)

 From Eqs. (1) and (2), we have

(vb+vw)×6=(vb−vw)×10

 vw=vb/4

 x=(vb+vw)×6=7.5vb

 Time taken by the motorboat to cover the same distance in still water is

 t=x/vb

=7.5vb/vb=7.5h

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