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

Options

A. 6
B. 7.5
C. 10
D. 15

Answer

B

Explanation

Let `v_w` be the velocity of water and `v_b` be the velocity of motor boat in still water . If is the distance covered , then as per question
`x=(v_(b)+v_w) xx 6 (v_b -v_w) xx10`
On solving , `v_w = (4b)/4 , :. [v_b +(4b)/4] xx 6 = 7.5 v_b`
Time taken by motor to cross the same distance in still water is
`t=(x)/v_b=(7.5v_b)/(v_b)=7.5` hours