Question

A person rowing at the rate of 5 km/h in still water , takes thrice as much time in going 40 km upstream as in going 40 km downstream . Find the speed of the stream .

Answer 1

Speed of the boat in still water = 5 km/h
Let the speed of stream = x km/h
∴ Speed of boat upstream = (5 − x) km/h
Speed of boat downstream = (5 + x) km/h
Time taken to row 40 km upstream = $\frac{40}{5-x}$
Time taken to row 40 km downstream = $\frac{40}{5+x}$
According to the given condition,
$$\begin{gathered} \frac{40}{5-x}=3\left(\frac{{\displaystyle 40}}{{\displaystyle 5+x}}\right) \\ \Rightarrow \frac{1}{5-x}=\frac{3}{5+x} \\ \Rightarrow 5+x=15-3x \\ \Rightarrow 4x=10 \\ \Rightarrow x=\frac{10}{4}=2.5\mathrm{km}/\mathrm{h} \end{gathered}$$
Therefore, the speed of the stream is 2.5 km/h.