A steamer goes downstream from one point to another in 9 hours.

It is given that the speed of the stream is $1 \mathrm{~km} / \mathrm{h}$.

Let the speed of the steamer in still water be $x \mathrm{~km} / \mathrm{h}$.

$\therefore$ Downstream speed $=(\mathrm{x}+1) \mathrm{km} / \mathrm{h}$

Upstream speed $=(\mathrm{x}-1) \mathrm{km} / \mathrm{h}$

The downstream and upstream distances are same; therefore, we have:

$9(\mathrm{x}+1)=10(\mathrm{x}-1)$

or $9 \mathrm{x}+9=10 \mathrm{x}-10$

or $\mathrm{x}=19$

$\therefore$ Speed of the steamer in still water $=19 \mathrm{~km} / \mathrm{h}$.

Distance between the ports $=9(19+1)=180 \mathrm{~km}$.