The boat passed along the river from pier A to pier B and returned. The boat went from A to B for 2 hours.

The boat passed along the river from pier A to pier B and returned. The boat went from A to B for 2 hours. 2.5 hours after the boat left the pier B, it still had to go 3 km to the pier A. Find the distance between the piers if the river flow is 3 km / h

Let x km / h be the boat’s own speed. Then its speed downstream will be equal to (x + 3) km / h, and upstream – (x – 3) km / h.

Since the boat passed from pier A to pier B in 2 hours, but it did not pass it back and for a longer time (2.5 hours), it means that from pier A to pier B it sailed with the current, and back – against.

The distance from A to B is 2 (x + 3) km, and the distance from B to A is (2.5 (x – 3) + 3) km. These distances are equal. Let’s equate them.

Let’s compose and solve the equation:

2 (x + 3) = 2.5 (x – 3) + 3;

2x + 6 = 2.5x – 7.5 +3;

2x – 2.5x = -7.5 + 3 – 6;

-0.5x = -10.5;

x = -10.5: (-0.5);

x = 21 (km / h).

Find the distance between the marinas by substituting the found speed of the boat into the left side of the equation:

2 * (x + 3) = 2 * (21 + 3) = 2 * 24 = 48 (km).

Answer: the distance between the marinas is 48 km.