The boat along the river in 5 hours sailed the same distance that it swims against the river in 8 hours.

The boat along the river in 5 hours sailed the same distance that it swims against the river in 8 hours. How many times is the boat’s own speed greater than the speed of the river flow?

1. Let us denote the speed of the boat through V, the speed of the river through W, and the distance through L. According to the condition of the problem, it is necessary to determine the ratio of the velocities V / W.

2. If the boat is sailing along the river, then the distance L is covered in 5 hours. I.e,
L / (V + W) = 5.

3. If the boat is sailing against the current of the river, then the distance L is covered in 8 hours. I.e,
L / (V – W) = 8.

4. Let’s divide these ratios one by another. We get: (V – W) / (V + W) = 5/8.

5. Divide the numerator and denominator of the fraction on the left side of the ratio by W. We get:
(V / W – 1) / (V / W + 1) = 5/8.

6. Multiply both sides of the relation by (V / W + 1) and expand the brackets. We get:
V / W – 1 = 5/8 * V / W + 5/8.

7. Received the equation: 3/8 * V / W = 1 + 5/8 = 13/8. Hence V / W = 8/3 * 13/8 = 13/3.

Answer: the boat’s own speed is (13/3) times the speed of the river flow.