Question

A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. If the speed of the stream is 2 kmph, find the speed of the boat in still water.

Answer 1

$$\begin{gathered} \text{Let the speed of the boat in still water be x km/hr.} \\ \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\text{speed of the stream is 2 km/hr.} \\ \therefore \mathrm{S}\text{peed upstream =}(x-2)\text{km/hr} \\ \text{Speed downstream =}(x+2)\text{km/hr} \\ \text{Time taken to go 8 km downstream =}\frac{8}{(x+2)}\text{hr} \\ \text{Time taken to go 8 km upstream =}\frac{8}{(x-2)}\text{hr} \\ \therefore \frac{8}{(x+2)}+\frac{8}{(x-2)}=1\frac{40}{60} \\ \Rightarrow \frac{8}{(x+2)}+\frac{8}{(x-2)}=\frac{100}{60} \\ \Rightarrow \frac{8(x-2)+8(x+2)}{(x-2)(x+2)}=\frac{5}{3} \\ \Rightarrow \frac{16x}{x^2-4}=\frac{5}{3} \\ \Rightarrow 3\times 16x=5(x^2-4) \\ \Rightarrow 48x=5x^2-20 \\ \Rightarrow 5x^2-48x-20=0 \\ \Rightarrow 5x^2-(50-2)x-20=0 \\ \Rightarrow 5x^2-50x+2x-20=0 \\ \Rightarrow 5x(x-10)+2(x-10)=0 \\ \Rightarrow (x-10)(5x+2)=0 \\ \Rightarrow x-10=0\text{or 5}x+2=0 \\ \Rightarrow x=10\text{or}x\text{=}\frac{-2}{5} \\ \Rightarrow x=10(\because \text{Speed cannot be a negative fraction}) \\ \therefore \mathrm{Speed\; of\; the\; boat\; in\; still\; water}\text{= 10 km/hr} \end{gathered}$$