## 16. Navigation

A ship is sailing along a river. After 6 hours, it returns to the starting point, having traveled a distance of 36 km on the map (naturally, the ship had to move in different directions at different times).

What is the speed of the ship, assuming it did not spend any time turning around, and the speed of the river current is $3 \mathrm{~km} / \mathrm{h}$?
16. Let $x$ (km/h) be the speed of the ship in still water. Then the speed of its movement downstream is $x+3$, and the speed of movement upstream is $x-3$. Since the total time spent is 6 hours, and the distances traveled downstream and upstream are clearly the same, we get

$$
18 /(x+3)+18 /(x-3)=6
$$

or

$$
x^{2}-6 x-9=0,
$$

i.e.,

$$
(x-3)^{2}-18=0, \text { or }(x-3-3 \sqrt{2})(x-3+3 \sqrt{2})=0 \text {. }
$$

Therefore, the speed of the ship is

$$
x=3+3 \sqrt{2} \approx 7.24 \text { km } / \text { h. }
$$