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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.

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Solution

## $\mathrm{Let}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{steamer}\mathrm{in}\mathrm{still}\mathrm{water}\mathrm{be}\mathrm{x}\mathrm{km}/\mathrm{h}.\phantom{\rule{0ex}{0ex}}\mathrm{Speed}\left(\mathrm{downstream}\right)=\left(x+1\right)\mathrm{km}/\mathrm{h}\phantom{\rule{0ex}{0ex}}\mathrm{Speed}\left(\mathrm{upstream}\right)=\left(x-1\right)\mathrm{km}/\mathrm{h}\phantom{\rule{0ex}{0ex}}\mathrm{Distance}\mathrm{covered}\mathrm{in}9\mathrm{hours}\mathrm{while}\mathrm{going}\mathrm{downstream}=9\left(x+1\right)\mathrm{km}\phantom{\rule{0ex}{0ex}}\mathrm{Distance}\mathrm{covered}\mathrm{in}10\mathrm{hours}\mathrm{while}\mathrm{going}\mathrm{upstream}=10\left(x-1\right)\mathrm{km}\phantom{\rule{0ex}{0ex}}\mathrm{But}\mathrm{both}\mathrm{of}\mathrm{these}\mathrm{distances}\mathrm{will}\mathrm{be}\mathrm{same}.\phantom{\rule{0ex}{0ex}}9\left(x+1\right)=10\left(x-1\right)\phantom{\rule{0ex}{0ex}}⇒9x+9=10x-10\phantom{\rule{0ex}{0ex}}⇒9+10=10x-9x\phantom{\rule{0ex}{0ex}}⇒19=x\phantom{\rule{0ex}{0ex}}⇒x=19\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{steamer}\mathrm{in}\mathrm{still}\mathrm{water}\mathrm{is}19\mathrm{km}/\mathrm{h}.\phantom{\rule{0ex}{0ex}}\mathrm{Distance}\mathrm{between}\mathrm{the}\mathrm{ports}=9\left(x+1\right)=9\left(19+1\right)=9×20=180\mathrm{km}$

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