# The motor ship goes downstream to the point of destination 160 km / h and after stopping returns to the point

**The motor ship goes downstream to the point of destination 160 km / h and after stopping returns to the point of departure. Find the speed of the current, if the speed of the ship in still water is 18 km / h, the stay lasts 6 hours, and the ship returns to the point of departure exactly one day after leaving it.**

Since the ship returns exactly one day later, it means that it is on the way for 24 hours.

Taking into account parking, travel time will be:

24 – 6 = 18 hours.

Let’s denote the speed of the river as x.

In this case, the downstream velocity will be 18 + x, and the upstream speed will be 18 – x.

We get the equation:

160 / (18 + x) + 160 / (18 – x) = 18 hours.

2880 – 160 * x + 2880 + 160 * x = 5832 – 18 * x ^ 2.

18 * x ^ 2 + 5760 – 5832 = 0.

18 * x ^ 2 – 72 = 0.

x ^ 2 = 72/18 = 4.

x = 2.

Answer: the speed of the river is 2 km / h.