1973 AMC 12 Problem 29
Attempt Problem 29 of the 1973 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1973 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
29.
Two boys start moving from the same point on a circular track but in opposite directions. Their speeds are ft. per sec. and ft. per sec. If they start at the same time and finish when they first meet at the point again, then the number of times they meet, excluding the start and finish, is
infinity
none of these
Answer: A
Small hint:
Because and are relatively prime, determine when both boys first complete whole numbers of laps
Big hint:
Before that finish time, meetings occur whenever their combined distance is another whole lap
Solution:
Let the track length be Since the first positive time when both boys are back at is : they have completed and laps. Their relative speed is so before time they meet at Thus there are meetings excluding the start and finish.
Therefore, the correct answer is A.
Problem 29 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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- 1972 AMC 12
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