A person rows a boat 10 kms along the stream in 30 minutes and returns to the starting point in 40 minutes. The speed of the stream is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2.5 km/h
Going along the stream (downstream), the stream adds to the boat’s speed; coming back against it (upstream), it takes away. So speed of the stream \(=\frac{\text{downstream speed}-\text{upstream speed}}{2}\).
Downstream: 10 km in 30 minutes \(=\frac{1}{2}\) hour
Upstream: 10 km in 40 minutes \(=\frac{2}{3}\) hour
Downstream speed \(\displaystyle =10\div\frac{1}{2}=20\,\mathrm{km/h}\)
Upstream speed \(\displaystyle =10\div\frac{2}{3}=15\,\mathrm{km/h}\)
Speed of the stream \(\displaystyle =\frac{20-15}{2}=2.5\,\mathrm{km/h}\)
The boat’s own speed in still water is \(\frac{20+15}{2}=17.5\,\mathrm{km/h}\), the figure in Option (1); the question asks for the stream’s speed.