The distance between berths A and B the raft sails in 18 hours, the boat against the current in 2 hours.

The distance between berths A and B the raft sails in 18 hours, the boat against the current in 2 hours. Find how many hours the boat will sail on the lake.

1. We take the speed of the water flow in the river as x (km / h), for y (km / h) – the speed of the boat in still water, z (kilometers) – the distance between the berths.

2. The speed of the river vessel when moving in the direction opposite to the direction of the water flow (y – x) km / h.

3. Let’s compose two equations:

x = z / 18;

(y – x) = z / 2;

4. Substitute x = z / 18 into the second equation:

y – z / 18 = z / 2;

y = z / 2 + z / 18 = 10z / 18 = 5z / 9;

5. We calculate how many hours a river vessel will sail the distance between berths on the lake: z: 5z / 9 = 9z / 5z = 1.8 hours.

Answer: a river vessel will sail the distance between the berths on the lake in 1.8 hours.