Question

Pratik takes 8 hours to travel 36 km down stream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.

Answer 1

Let the speed of water current = y km/h
Speed of boat in still water = 12 km/h
Speed upstream = $12-y$
Speed downstream = 12 + y
Distance travelled = 36 km downstream and 36 km upstream
$$\begin{gathered} \mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}} \\ \Rightarrow \mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}} \end{gathered}$$
$$\begin{gathered} \frac{36}{12-y}+\frac{36}{12+y}=8 \\ \Rightarrow 36\left[\frac{1}{12-y}+\frac{1}{12+y}\right]=8 \\ \Rightarrow \frac{12+y+12-y}{144-y^2}=\frac{1}{4} \\ \Rightarrow \frac{24}{144-y^2}=\frac{{\displaystyle 1}}{{\displaystyle 4}} \\ \Rightarrow 144-y^2=24\times 4 \\ \Rightarrow y^2=36 \\ \Rightarrow y^2-36=0 \\ \Rightarrow y=\pm 6 \end{gathered}$$
Speed cannot be negative so, the speed of water current = 6 km/h.