Question

A boat whose speed in $15km/hr$ in still water goes $30$ km downstream and comes back in a total of $4$ hours $30$ minutes. the speed of the stream (in km/hr) is :

Answer 1

Total time is given$=4hours30minutes=4.5hours$

$t_d+t_u=4.5$

Let's say the speed of the stream is $u$ and distance $d=30km$ then,

Time taken to travel downstream $\left(t_d\right)=\frac{30}{15+u}$ ......(1)

Time taken to travel upstream $\left(t_u\right)=\frac{30}{15-u}$ .....(2)

Adding equation (1) and (2),

$t_d+t_u=\frac{30}{15+u}+\frac{30}{15-u}$

$4.5=\frac{30(15-u+15+u)}{(15-u)(15+u)}$

On multiplying by $2$ in both sides, we get

$4.5\times 2=\frac{2\times 30\times 30}{({15}^2-u^2)}$

$225-u^2=200$

$u^2=25$

$u=5km/hr$

Hence, the speed of the stream is $5km/hr$.