Question

A motor boat whose speed is $18km/h$ in still water takes $1$ hr more to go $24km$, upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

Given the speed of boat $=18km/hr$.

Let the speed of the stream $=xkm/hr$

For upstream For downstream

time $=\frac{24}{18-x}$ time $=\frac{24}{18+x}$

From condition

Time upstream = time downstream $+1$

$\frac{24}{18-x}=\frac{24}{18+x}+1$

$18\times 24+24x=24\times 18-24x+(18-x)(18+x)$

$x^2+48x-324=0$

$x=\frac{-48\pm \sqrt{(48{)}^2+4\times 324}}{2}$

$x=\frac{-48\pm 60}{2}$

$x=6$ or $x=-54$

Since $x$ is a speed so it cannot be negative

So $x=6$ is right value

thus speed of stream $\Rightarrow x=6km/hr$