Question

A motorboat can move as fast as 30 km/h in still water. A man travels from one coastal town to another coastal town in 6 hours while going downstream. When he returns (upstream), he covers the same distance in 8 hours. What is the speed of the stream?

• A. $4$ km/h
• B. $\frac{30}{7}$ km/h
• C. $\frac{35}{6}$ km/h
• D. $\frac{17}{4}$ km/h

Answer 1

The correct option is B $\frac{30}{7}$ km/h

Let the speed of the stream be $x$ km/h.
Speed of motorboat = 30 km/h

Downstream speed = $30+x$ km/h
Upstream speed = $30-x$ km/h

Distance = Speed x time.

Here, the diatance covered is the same. Hence

$6(30+x)=8(30-x)\Rightarrow 180+6x=240-8x\Rightarrow 6x+8x=240-180\Rightarrow 14x=60\Rightarrow x=\frac{60}{14}\Rightarrow x=\frac{30}{7}\text{km/h}$

Hence, the speed of the stream is $\frac{30}{7}$ km/h.