Question

A steamer goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed of the steamer in still water and the distance between the ports.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{steamer}\mathrm{in}\mathrm{still}\mathrm{water}\mathrm{be}\mathrm{x}\mathrm{km}/\mathrm{h}. \\ \mathrm{Speed}\left(\mathrm{downstream}\right)=(x+1)\mathrm{km}/\mathrm{h} \\ \mathrm{Speed}\left(\mathrm{upstream}\right)=(x-1)\mathrm{km}/\mathrm{h} \\ \mathrm{Distance}\mathrm{covered}\mathrm{in}9\mathrm{hours}\mathrm{while}\mathrm{going}\mathrm{downstream}=9(x+1)\mathrm{km} \\ \mathrm{Distance}\mathrm{covered}\mathrm{in}10\mathrm{hours}\mathrm{while}\mathrm{going}\mathrm{upstream}=10(x-1)\mathrm{km} \\ \mathrm{But}\mathrm{both}\mathrm{of}\mathrm{these}\mathrm{distances}\mathrm{will}\mathrm{be}\mathrm{same}. \\ 9(x+1)=10(x-1) \\ \Rightarrow 9x+9=10x-10 \\ \Rightarrow 9+10=10x-9x \\ \Rightarrow 19=x \\ \Rightarrow x=19 \\ \mathrm{Therefore},\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{steamer}\mathrm{in}\mathrm{still}\mathrm{water}\mathrm{is}19\mathrm{km}/\mathrm{h}. \\ \mathrm{Distance}\mathrm{between}\mathrm{the}\mathrm{ports}=9(x+1)=9(19+1)=9\times 20=180\mathrm{km} \end{gathered}$$