Two friends run a 3-kilometer race along a circular course of length 300 meters. If their speeds are in the ratio 3:2, the number of times the winner passes the other is __________.
Explanation:
Since the ratio of their speeds is 3 : 2, they will meet at only one point on the circular track and that point will be the starting point.
Hence, when they meet for the first time, the faster person travels 3 rounds, the slower person would travel 2 rounds. i.e., when the faster person travels 3 × 300 = 900 meters, they meet once.
∴ When the faster person travels 2700 (3 × 900) meters, they would have met 3 times.
To meet for the 4th time faster person needs to travel 900 meters more, but he has only 300 meters of the race left. ∴ Now the faster person would complete the race before they meet for the 4th time.
Hence, 3.
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