A motor boat travels the distance from one village to another along the river in 2 hours

A motor boat travels the distance from one village to another along the river in 2 hours, versus in 3 hours. The speed of the river is 1.5 km / h. Find the distance between the points.

The proper speed (in km / h) of a motor boat is denoted by x.
According to the condition of the assignment, the speed of the river flow is 1.5 km / h. Therefore, when a motor boat moves along the river, its speed increases by the speed of the river and becomes equal to (x + 1.5) km / h. In 2 hours, a motor boat moving along the river will cover 2 * (x + 1.5) km.
Likewise, when a motor boat moves against the flow of a river, its speed decreases by the speed of the river flow and becomes equal to (x – 1.5) km / h. In 3 hours, a motor boat moving against the stream of the river will cover 3 * (x – 1.5) km.
The distances found are equal to the distance from one village to another. We have 2 * (x + 1.5) = 3 * (x – 1.5). Let’s solve this equation: 2 * x + 2 * 1.5 = 3 * x – 3 * 1.5 or x = 4.5 + 3 = 7.5.
Therefore, the distance between points (villages) is 2 * (7.5 + 1.5) = 2 * 9 = 18 km.
Answer: 18 km.