1967 AMC 12 Problem 27
Attempt Problem 27 of the 1967 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 1967 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
Two candles of the same length are made of different materials so that one burns out completely at a uniform rate in hours and the other in hours. At what time P.M. should the candles be lighted so that, at P.M., one stub is twice the length of the other?
Answer: C
Small hint:
Let be the number of hours the candles burn before P.M.
Big hint:
Their remaining fractions are and
Solution:
After hours, the faster and slower candles have fractions and remaining. The slower stub must be twice the faster: Thus hours minutes. Counting back from P.M. gives P.M.
Therefore, the correct answer is C.
Problem 27 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
- 1964 AMC 12
- 1965 AMC 12
- 1966 AMC 12
- 1968 AMC 12
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