Question

A motor boat whose speed is $15$ km/hr in still water goes $30$ km downstream and comes back in $4$ hours $30$ minutes. Determine the speed of the stream.

• A. $12$ km/hr
• B. $9$ km/hr
• C. $5$ km/hr
• D. $3$ km/hr

Answer 1

The correct option is C $5$ km/hr

Let the speed of the stream be $x$ km/hr

Then Speed of boat downstream $=(15+x)$ km/hr
Speed of boat upstream $=(15-x)$ km/hr
Therefore, $\frac{30}{15+x}+\frac{30}{15-x}=4\frac{1}{2}=\frac{9}{2}$
$\Rightarrow \frac{30(15-x)+30(15+x)}{(15+x)(15-x)}=\frac{9}{2}$

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

$\Rightarrow 200=225-x^2$
$\Rightarrow x^2=25$

$\Rightarrow x=5$ km/hr