Question

A boat takes $2$ hours to go $8km$ and come back in still water lake. With velocity of $4km/hr$, the time taken for going upstream of $8km$ and coming back is

• A. 140 minutes
• B. 150 minutes
• C. 160 minutes
• D. 170 minutes

Answer 1

The correct option is C 160 minutes

$\frac{8}{v_{rm}}+\frac{8}{v_{rm}}=2\Rightarrow v_{mr}=8km/h$
$\Rightarrow t=\frac{8}{v_{mr}+v_r}+\frac{8}{v_{mr}-v_r}$
$\Rightarrow t=\frac{8(v_{mr}-v_r+v_{mr}+v_r)}{v_{mr}^2-v_r^2}=\frac{16v_{mr}}{v_{mr}^2-v_r^2}$
$\frac{16\times 8}{64-16}=\frac{16\times 8}{48}h=\frac{8}{3}\times 60=160min$