There are 8 equitant points A, B, C, D, E, F, G and H in the clockwise direction on the periphery of a circle. In a time, interval t, a person reaches from A to C with uniform motion while another person reaches the point E from the point B during the same time interval with uniform motion. Both the persons move in the same direction along the circumference of the circle and start at the same instant. How much time after the start, will the two persons’ meet each other?

To solve this, let the distance between any two adjacent points be 1 unit. The total circumference of the circle is 8 units since there are 8 equidistant points.

Person 1 moves from A to C in time t. This is a distance of 2 units. Therefore, the speed of Person 1 is 2 units per t.

Person 2 moves from B to E in time t. This is a distance of 3 units. Therefore, the speed of Person 2 is 3 units per t.

At the start, Person 1 is at point A and Person 2 is at point B. Since they move clockwise, Person 2 is 1 unit ahead of Person 1. Alternatively, looking at the direction of motion, Person 1 is 7 units behind Person 2.

To find when they meet, we calculate the relative speed. Since they move in the same direction, the relative speed of Person 2 with respect to Person 1 is 3 minus 2, which equals 1 unit per t.

Person 2 needs to cover the entire circumference of 8 units minus the initial 1 unit gap to catch up with Person 1 from behind, or more simply, Person 2 is gaining 1 unit of distance every t.

Since Person 1 starts at A and Person 2 starts at B, Person 2 is 1 unit ahead. For them to meet, Person 2 must complete a full lap and close the gap. However, it is simpler to look at the positions: At time 0: P1 is at 0, P2 is at 1. At time t: P1 is at 2, P2 is at 4. At time 2t: P1 is at 4, P2 is at 7. At time 7t: Distance covered by P1 is 7 times 2 which equals 14 units. Distance covered by P2 is 7 times 3 which equals 21 units.

Starting from A, 14 units clockwise lands P1 at point G. Starting from B (which is 1 unit from A), 21 units clockwise is 1 plus 21 which equals 22 units from A. In a circle of 8 units, 22 units is 22 divided by 8, which leaves a remainder of 6. The 6th point from A is G. Since both are at point G at time 7t, they meet at 7t.