Two points move along a circle of length 120m with a constant speed. If they move in different directions, then they meet every 15 seconds. When going in the same direction, one point catches up to the second every 60 seconds. Find the speeds of the points.

Total Distance covered in one round of circle = 120 m

Let x and y be the speeds of the two points.

When two points are moving in opposite directions, they meet in every 15 seconds. This means they cover 120 m in 15 seconds. They are moving in opposite directions, so the relative speed will be equal to the sum of speeds of both points. So we can set up the equation as:

x + y = 120/15
x + y = 8 

This means, sum of their speeds is 8 m/s

When moving in the same direction, one point catches the other point every 60 seconds. We can set up the equation for this case as:

x - y = 120/60
x - y = 2

This means, difference of their speeds is 2m/s

Adding both equations we get:

x+ y +x - y = 8 + 2

2x = 10

x = 5 m/s

x + y =8
This means, y = 3 m/s

Thus, the speed of the two points is 5 m/s and 3 m/s