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.

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