Question

A motor boat can travel at $10$ km/h in still water. It travelled $91$ km downstream in a river, then returned taking altogether $20$ hours. Find the rate of flow of the river.

• A. $3$ km/h
• B. $5$ km/h
• C. $6$ km/h
• D. $8$ km/h

Answer 1

The correct option is A $3$ km/h

Let the flow of the river be $x$ km/h.
Then, speed downstream $=(10+x)$ km/h
and speed upstream $=(10-x)$ km/h
$\therefore \frac{91}{(10+x)}+\frac{91}{(10-x)}=20$
$\Rightarrow 91\left[\frac{20}{(10+x)(10-x)}\right]=20$
$\Rightarrow (10+x)(10-x)=91$
$\Rightarrow 100-x^2=91$
$\Rightarrow x^2=9$
$\Rightarrow x=3$
Hence, rate of flow of the river $=3$ km/h