The speed of water current is half the speed of a motor boat. The motor boat travels 15 km downstream in 1 hour. Then the time taken to returrn to the starting point is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3 hours
Let speed of motor boat in still water = $b$ km/h
Speed of water current = $\frac{b}{2}$ km/h
Downstream speed = $b + \frac{b}{2} = \frac{3b}{2}$
Time downstream = 1 hour, Distance = 15 km
$\text{Distance} = \text{Speed} \times \text{Time} \Rightarrow 15 = \frac{3b}{2} \cdot 1 \Rightarrow b = 10$ km/h
Upstream speed = $b - \frac{b}{2} = \frac{10}{2} = 5$ km/h
Time to return upstream = $\frac{\text{Distance}}{\text{Speed}} = \frac{15}{5} = 3$ hours