# 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?

May 26, 2021 | education

| 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.