Question

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..........

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

Answer 1

Answer: (D)

If $v_w$ be the velocity of water and $v_b$ be the velocity of motorboat in still water.
The distance covered by motorboat in moving downstream in $6h$ is
$x=\left(v_b+v_w\right)\times 6$...(i)
Same distance covered by motorboat in moving upstream in $10h$ is
$x=\left(v_b-v_w\right)\times 10$...(ii)
From Eqs. (i) and (ii), we have
$\left(v_b+v_w\right)\times 6=\left(v_b-v_w\right)\times 10$
$v_w=\frac{v_b}{4}$
$\therefore x=\left(v_b+v_w\right)\times 6=7.5v_b$
Time taken by the motorboat to cover the same distance in still water is
$t=\frac{x}{v_b}=\frac{7.5v_b}{v_b}=7.5h$