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