Question

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

Answer 1

Given :

Speed of boat in still water $=15km/hr$

Let $x$ be speed of the stream in $km/hr$
Speed of the boat upstream $=15-x$
Speed of the boat down stream $=15+x$

Time taken for upstream $T_1=\frac{30}{15-x}$

Time taken for downstream $T_2=\frac{30}{15+x}$

Given, $T_1+T_2=\frac{9}{2}$

$=\frac{30}{15-x}+\frac{30}{15+x}=\frac{9}{2}$

$=30(\frac{1}{15-x}+\frac{1}{15+x})=\frac{9}{2}$

$=30\left(\frac{15+x÷15-x}{(15-x)(15+x)}\right)=\frac{9}{2}$

$=\frac{30\times 30}{225-x^2}=\frac{9}{2}$

$=\frac{100}{225-x^2}=\frac{1}{2}$

$\Rightarrow 225-x^2=200$

$\Rightarrow x^2=25$

$\Rightarrow x=5$ ....($\because x$ is +ve)

$\Rightarrow x=5km/hr$

Speed of the stream $=5km/hr$.