Question

a man takes 6 hours to row 96 km upstream and 5 hours to cover 120 km downstream. find the speed at which the river is flowing and the speed of the boat in still water.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{boat}\mathrm{in}\mathrm{still}\mathrm{water}=x\mathrm{km}/\mathrm{hr} \\ \mathrm{and}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{in}\mathrm{the}\mathrm{river}=y\mathrm{km}/\mathrm{hr} \\ \mathrm{then}\mathrm{speed}\mathrm{upstream}=\left(x-y\right)\mathrm{km}/\mathrm{hr} \\ \mathrm{and}\mathrm{speed}\mathrm{down}\mathrm{stream}=\left(x+y\right)\mathrm{km}/\mathrm{hr} \\ \mathrm{then},\mathrm{time}\mathrm{taken}\mathrm{by}\mathrm{the}\mathrm{boat}\mathrm{to}\mathrm{cover}96\mathrm{km}\mathrm{upstream}=\frac{96}{\left(x-y\right)}\mathrm{hr} \\ \mathrm{The}\mathrm{time}\mathrm{taken}\mathrm{by}\mathrm{the}\mathrm{boat}\mathrm{to}\mathrm{cover}120\mathrm{km}\mathrm{downstream}=\frac{120}{\left(x+y\right)}\mathrm{hr} \\ \mathrm{Therefore},\mathrm{according}\mathrm{to}\mathrm{question}: \\ \frac{96}{x-y}=6\mathrm{and}\frac{120}{x+y}=5 \\ \Rightarrow 6\left(x-y\right)=96\mathrm{and}5\left(x+y\right)=120 \\ \Rightarrow x-y=16............\left(1\right)andx+y=24..............\left(2\right) \\ \mathrm{Adding}\left(1\right)\&\left(2\right),\mathrm{we}\mathrm{get}, \\ 2x=40 \\ \Rightarrow x=20 \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get}, \\ 20-y=16 \\ \Rightarrow 20-16=y \\ \Rightarrow y=4 \\ \mathrm{Hence},\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{boat}\mathrm{in}\mathrm{still}\mathrm{water}=20\mathrm{km}/\mathrm{hr}. \\ \mathrm{And}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{water}\mathrm{in}\mathrm{the}\mathrm{river}=4\mathrm{km}/\mathrm{hr}. \end{gathered}$$