Question

The speed of a boat in still water is $15$ km/hr. It goes $30$ km upstream and return downstream to the original point in $4$ hrs $30$ minutes. Find the speed of the stream(in km/hr).

Answer 1

$\Rightarrow$ Let speed of stream be $xkm/hr$

$\Rightarrow$ Downstream speed $=(15+x)km/hr$

$\Rightarrow$ Upstream speed $=(15-x)km/hr$

$\therefore$ $\frac{30}{15+x}+\frac{30}{15-x}=4\frac{1}{2}$

$\therefore$ $\frac{450+450}{225-x^2}=4\frac{1}{2}$

$\Rightarrow$ $\frac{900}{225-x^2}=\frac{9}{2}$

$\Rightarrow$ $9x^2=225$

$\Rightarrow$ $x^2=25$

$\therefore$ $x=5$

$\therefore$ Speed of stream is $5km/hr.$