The distance between quays A and B along the river is exactly 36 km. A raft sailed from A to B

The distance between quays A and B along the river is exactly 36 km. A raft sailed from A to B, and a boat departed from B to A after 8 hours. They arrived at their destinations at the same time. What is the speed of the raft if the boat’s own speed is 12 km / h?

Let v km / h be the speed of the river. Since the raft’s own speed is zero, it moves with the speed of the river v and travels a distance of 36 km in a time t equal to

t = 36 / v.

The speed of a boat moving against the stream of the river at its own speed of 12 km / h is (12 – v) km / h. The boat covered a distance of 36 km in time (t – 8) h. Then

t – 8 = 36 / (12 – v).

Substitute the expression for determining the time from the first equation into the second equation and find the speed of the raft:

v1 = 3 km / h;

v2 = 18 km / h.

Of the two results obtained, the value of 18 km / h does not satisfy the conditions of the problem, since at such a speed, a boat moving against the stream of the river will not be able to reach the destination.

Thus, the speed of the river is 3 km / h.