Two boats sailed up the river between two piers and the first boat overtook the second by 10 minutes.

Two boats sailed up the river between two piers and the first boat overtook the second by 10 minutes. Then they swam back downstream. How long will the first boat overtake the second, having covered the same distance? The speed of the river is 1 m / s, the speed of boats relative to the water is 9 m / s and 7 m / s.

Two boats originally moved up the river, that is, against the current, which means their speed was equal to:

9 – 1 = 8 m / s and 7 – 1 = 6 m / s.

At the same time, the first boat overtook the second by 10 minutes or 10 * 60 = 600 s.

Let’s say the distance between the piers is x m, then we can make the following equation:

x / 8 + 600 = x / 6,

(x + 4800) / 8 = x / 6,

6 * x + 28800 = 8 * x,

2 * x = 28800,

x = 14400 (m).

Moving along the river, the speed of the boats will be:

9 + 1 = 10 m / s and 7 + 1 = 8 m / s.

At this speed, the first boat will make its way back in:

14400: 10 = 1440 s,

and the second boat for:

14400: 8 = 1800 s.

This means that the first boat will overtake the second by:

1800 – 1440 = 360 s or 6 min.