## Circular race: When there are three runners around the circular track

Runners A, B and C running around a circular track with respective speeds a, b and c such that `a > b > c`. They start simultaneously and if the length of the race is 'L'.

**Same Direction:** Time taken to meet them for the first time along anywhere on the track `= "LCM" [L/(a - b), L/(b - c)]`

Time taken to meet them for the first time at the starting point is `= "LCM" [L/a, L/b, L/c]`

**Opposite direction:** If A is running clockwise while B and C are running anticlockwise;

Time taken to meet them for the first time along anywhere on the track `= "LCM" [L/(a + b), L/(a + c)]`

Time taken to meet them for the first time at the starting point is `= "LCM" [L/a, L/b, L/c]`

### Concept review questions

`= "LCM" [360, 240, 180] = 720 sec`

Divide the circular track into 10 equal distances.

Let the length of the track is 10 units.

When Joy cover 2 units counterclockwise and Ajo covered 3 units clockwise (as per diagram) they will meet at first (at point C)

For the meeting they took 12.5 seconds.

From the point C if Joy covers 2 units more on counter clockwise direction and Ajo covers 3 units more on clockwise direction then they will be in diametrically opposite positions.

Ie, for this additional movement, they require another 12.5 seconds

Therefore the total time required to become diametrically opposite is `12.5 + 12.5 = 25 sec`