From A to B the raft sails along the river in 40 hours, and the boat in 4 hours. How long will it take for the boat to return to A?

The speed of the raft is equal to the speed of the river and we will denote it by the letter x. So the distance from A to B is 40 * x.

Let the boat’s own speed be equal to y, then from A to B along the river it floats at a speed (x + y) and the distance between these points can be written as follows:

4 * (x + y).

We get the equation:

40 * x = 4 * (x + y),

40 * x = 4 * x + 4 * y,

4 * y = 36 * x,

y = 9 * x.

This means that the speed of the boat downstream will be 9 * x + x = 10 * x.

Moving back, that is, against the current, the speed of the boat will be 9 * x – x = 8 * x.

Suppose the boat will spend T hours on the way back, therefore:

4 * 10 * x = 8 * x * T,

40 = 8 * T,

T = 5 (hours).

Answer: 5 hours.