1. Ivan and Petr are running in different directions on circular tracks with a common center, and initially, they are at the minimum distance from each other. Ivan completes one full circle every 20 seconds, while Petr completes one full circle every 28 seconds. After what least amount of time will they be at the maximum distance from each other?
Answer: $35 / 6$ seconds.

Solution. Ivan and Petr will be at the minimum distance from each other at the starting points after the LCM $(20,28)=140$ seconds. During this time, Ivan will complete 7 laps, and Petr will complete 5 laps relative to the starting point. Consider this movement in a reference frame where Petr is stationary, then Ivan will complete 12 laps. Therefore, after 140: 24 = 35/6 seconds, Ivan will run half a lap. At this moment, they will be at the maximum distance from each other for the first time.

## Criteria. Only the answer: 1 point.