Question

The speed of a boat in still water is $15$ km/hr. It can go $30$ km upstream and return downstream to the original point in $4$ hrs $30$ min. The speed of the stream is:

• A. $5$ km / hr
• B. $8$ km/ hr
• C. $10$ km/hr
• D. $15$ km/hr

Answer 1

The correct option is A $5$ km / hr

Let the speed of the stream be $x$.
Hence, speed of the boat in upstream be $15-x$ and in down stream be $15+x$.
Hence, $\frac{30}{15-x}+\frac{30}{15+x}=4\frac{1}{2}$

$30\left(\frac{15-x+15+x}{225-x^2}\right)=\frac{9}{2}$
$20\left(\frac{30}{225-x^2}\right)=3$
$600=675-3x^2$
$x^2=25$
$\therefore x=\pm 5$
Hence, speed of the stream is $5$ km/hr.