# Task No. 5.1

## Condition:

A Dog, a Cat, and a Mouse are running around a circular lake. They all started simultaneously in the same direction from the same point and finished at the same time, each running at a constant speed. The Dog ran 12 laps, the Cat ran 6 laps, and the Mouse ran 4 laps. How many total overtakes were made from the start to the finish?

If two or more overtakes occur simultaneously, each overtake is counted separately. The start and finish moments are not counted as overtakes.
# Answer: 13

## Exact match of the answer -1 point

## Solution.

At the moment when the faster runner catches up with the slower one, he is ahead by one lap. The Dog has lapped the Cat by 6 laps, meaning it has caught up with her 6 times, with the last catch-up at the finish line not counting as a lap, so the Dog has lapped the Cat 5 times. The Dog has lapped the Mouse by 8 laps, meaning it has caught up with the Mouse 7 times. The Cat has lapped the Mouse by 2 laps, completing 1 lap. In total, the animals have completed $5+7+1=13$ laps.

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