The distance between the two berths of the kayak sails along the river in 30 minutes, and against the stream in 40 minutes

The distance between the two berths of the kayak sails along the river in 30 minutes, and against the stream in 40 minutes. River flow speed 50m / min. What is the distance between the two berths?

Let’s assume that the kayak’s own speed is x m / min.

The speed of the river flow, according to the condition of the problem, is 50 m / min, therefore the speed of the kayak along the river will be (x + 50) m / min, and against the current the kayak will swim at a speed of (x – 50) m / min.

Thus, the path of the kayak along the river is (x + 50) * 30, and the return path will be

(x – 50) * 40. We get the equations:

(x + 50) * 30 = (x – 50) * 40,

30 * x + 1500 = 40 * x – 2000,

10 * x = 3500,

x = 3500: 10,

x = 350.

If the kayak’s own speed is 350 m / min, then the distance between the berths is:

(350 + 50) * 30 = (350 – 50) * 40 = 12000 (m) = 12 (km).