Question

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

Answer 1

It is given that speed of motor boat in still water is $15km/hr$ and total distance travelled is $30km$.

Let the speed of the stream be $xkm/hr$ then the speed upstream is $(15-x)km/hr$ and speed downstream is $(15+x)km/hr$.

It is also given that total time taken is $4$ hours $30$ minutes, therefore,

Time taken to row down the stream is $\frac{30}{15+x}$ and

Time taken to row up the stream is $\frac{30}{15-x}$

Thus, we have

$\frac{30}{15+x}+\frac{30}{15-x}=4\frac{1}{2}$

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

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

$\Rightarrow \frac{450-30x+450+30x}{(15{)}^2-x^2}=\frac{9}{2}(\because a^2-b^2=(a+b\left)\right(a-b\left)\right)$

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

$\Rightarrow 2\times 900=9(225-x^2)$

$\Rightarrow 1800=9(225-x^2)$

$\Rightarrow 225-x^2=\frac{1800}{9}$

$\Rightarrow 225-x^2=200$

$\Rightarrow x^2=225-200$

$\Rightarrow x^2=25$

$\Rightarrow x=\pm \sqrt{25}$

$\Rightarrow x=\pm 5$

Since the speed cannot be negative thus, $x=5$.

Hence, the speed of the stream is $5km/hr$.