# Two points, moving in a circle in the same direction, meet every 56 minutes, moving in opposite directions

Two points, moving in a circle in the same direction, meet every 56 minutes, moving in opposite directions, every 8 minutes. Find the speed of each point and the circumference if it is known that in 1 s the first point passes 1/12 meter more than the second.

We convert minutes to seconds:
8 minutes = 8 * 60 = 480 seconds;
56 minutes = 56 * 60 = 3360 seconds.

In order for the points moving in the same direction to meet, it is necessary that the 1st point overtake the 2nd by one circle, this happens in 3360 seconds. The rate of change in the distance between them is equal to (1/12) m / s.
Find the circumference:
L = 1/12 * 3360 = 280 m.

Let’s designate the speed of the 1st point x, then the 2nd – (x – 1/12). When moving in the opposite direction, the points cover the distance L in 480 seconds:
(x + x – 1/12) * 480 = 280;
2 * x = 8/12;
x = 1/3 m / s – the speed of the first point.
1/3 – 1/12 = 1/4 m / s – speed of the second point.

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