A person crosses a 1 km wide river with a speed of 5km/hr through the minimum path in 15 minutes. The velocity of flow of river in km/hr, will be

$$\begin{gathered} \text{Shortest possible path,s}=1\mathrm{km} \\ \text{Time taken,}\mathrm{t}=15\min =0.25\mathrm{hr} \\ \text{Speed in the direction of shortest path,}\frac{\mathrm{s}}{\mathrm{t}}=\sqrt{{\mathrm{v}}^2-{\mathrm{u}}^2} \\ \text{Where,}\mathrm{v}=5{\mathrm{kmh}}^{-1}\text{velocity of boat,}\mathrm{u}\text{velocity of river.} \\ \frac{\mathrm{s}}{\mathrm{t}}=\sqrt{{\mathrm{v}}^2-{\mathrm{u}}^2} \\ \frac{1}{0.25}=\sqrt{5^2-{\mathrm{u}}^2} \\ \mathrm{u}=3{\mathrm{kmh}}^{-1} \\ \text{Hence, velocity of river is }3{\mathrm{kmh}}^{-1} \end{gathered}$$