Question

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

Answer 1

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

Then, Speed downstream $=(15+x)$ km/hr
Speed upstream $=(15-x)$ km/hr
Time taken by the boat to go $30km$ upstream $=\frac{30}{15-x}hours$
time taken by the boat to return $30km$ downstream $=\frac{30}{15+x}hours$ hours

It is given that the boat returns to the same point in $4$ hours $30$ minutes

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

$\Rightarrow \frac{450+30x+450-30x}{225-x^2}=\frac{9}{2}\Rightarrow \frac{900}{225-x^2}=\frac{9}{2}\Rightarrow 225-x^2=200\Rightarrow x^2=25\Rightarrow x=\pm 5$

But the speed of the stream can never be negative

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