The motor boat covered 90 km along the river in 6 hours, and against the river in 10 hours.

The motor boat covered 90 km along the river in 6 hours, and against the river in 10 hours. How long will it take for the raft to sail the same distance along the river?

Let’s say that the speed of the motorboat is x km / h, and the speed of the river is y km / h.
Then, according to the condition of the problem, we can compose the following system of two equations:
(x + y) * 6 = 90,
(x – y) * 9 = 90.
From the first equation we get:
x + y = 90: 6,
x + y = 15,
y = 15 – x.
Substitute this value into the second equation:
(x – (15 – x)) * 9 = 90,
x – 15 + x = 10,
2 * x = 10 + 15,
x = 25: 2,
x = 12.5 (km / h) – speed of the motor boat,
15 – 12.5 = 2.5 (km / h) – river flow speed.
Since the raft moves at the speed of the current, the given distance will be covered by the raft in:
90: 2.5 = 36 hours