Question

A Sailor goes $8$ km downstream in $40$ min and comes back in $1$ hour. Find the speed of the sailor in still water and speed of current.

Answer 1

Let speed of sailor in still water be $ukm/hr$

Let speed of current be $vkm/hr$

Upstream speed$=(u-v)km/hr$

Downstream Speed$=(u+v)km/hr$

$\frac{8}{u+v}=\frac{40}{60}$

$=\frac{8}{u+v}=\frac{2}{3}⟶\left(i\right)$

$\frac{8}{u-v}=1⟶\left(ii\right)$

$\left(i\right)÷\left(ii\right)$

$\frac{u-v}{u+v}=\frac{2}{3}$

$3u-3v=2u+2v$

$u=5v$

Putting $u=5v$ in equation$1$

$\frac{2}{5v-v}=1$

$8=4v$

$v=2km/hr$

$\therefore u=10km/hr$