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

Options

A. 9 hours
B. 7.5 hours
C. 6.5 hours
D. 8 hours

Answer

B

Explanation

Let `v_(w)` be the velocity of water and `v_(b)` be the velocity of motorboat in still water.
The distance x covered by the motorboat in moving downstream in 6 h is
`x=(v_(b)+v_(w))xx6` . . . (i)
Same distance x covered by the motorboat in moving upstream in10 h is
`x=(v_(b)-v)_(w)xx10` . . . (ii)
Equating (i) and (ii), we get
`(v_(b)+v_(w))xx6=(v_(b)-v_(w))xx10`
`v_(w)=(v_(b))/(4):.x=(v_(b)+v_(w))xx6=7.5v_(b)`
Time taken by the motorboat to cover the same distance in still water is
`t=(x)/(v_(b))=(7.5v_(b))/(v_(b))=7.5` hours