#### Answer

90 minutes

#### Work Step by Step

Two people are jogging on a circular track. Person A takes 15 minutes to jog around the track. Person B takes 18 minutes to jog around the track. If they both start at the same time (same spot), they will be at that spot at the same time again in 90 minutes.
We can look at the multiples of 15 and 18 and see when they match. The first match from the lists of multiples will be when they are at the starting point together again.
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
Multiples of 18: 18, 36, 48, 64, 72, 90, 108, 126, ...
The first match we see is at 90 minutes.