Question

A motorboat, whose speed is $15$ km/hr in still water goes $30$ km downstream and comes back in a total of $4$ hours $30$ minutes. The speed of the stream is

• A. $4$ km/hr
• B. $5$ km/hr
• C. $6$ km/hr
• D. $10$ km/hr

Answer 1

The correct option is B $5$ km/hr

Let the speed of the stream be $x$ km/hr.
Then, speed downstream $=(15+x)$ km/hr
and speed upstream $=(15-x)$ km/hr
$\therefore \frac{30}{(15+x)}+\frac{30}{(15-x)}=4\frac{1}{2}$
$\Rightarrow 30\left(\frac{30}{(15+x)(15-x)}\right)=\frac{9}{2}$
$\Rightarrow (15+x)(15-x)=200$
$\Rightarrow 225-x^2=200$
$\Rightarrow x^2=25$
$\Rightarrow x=5$
Hence, speed of the stream $=5$ km/hr