1967 AMC 12 第 27 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
27.
两支等长的蜡烛由不同材料制成，其中一支以均匀速度在 小时内燃尽，另一支在 小时内燃尽。应在下午几点点燃蜡烛，才能使下午 点时一支蜡烛的剩余长度是另一支的两倍？
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?
小提示：
设蜡烛在下午 点前燃烧的小时数为
Let be the number of hours the candles burn before P.M.
大提示：
它们剩余的比例分别为 与
Their remaining fractions are and
解答：
经过 小时后，燃烧较快和较慢的蜡烛剩余比例分别为 与 。较慢蜡烛的剩余长度必须是较快蜡烛的两倍：因此 小时 分钟。从下午 点向前推，得到下午 。
因此，正确答案是 C。
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.
其他年份的第 27 题
- 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
- 1969 AMC 12
- 1970 AMC 12
- 1971 AMC 12
- 1972 AMC 12
- 1973 AMC 12
- 1974 AMC 12
- 1975 AMC 12
- 1976 AMC 12
- 1977 AMC 12
- 1978 AMC 12
- 1979 AMC 12
- 1980 AMC 12
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- 1982 AMC 12
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- 1986 AMC 12
- 1987 AMC 12
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- 1989 AMC 12
- 1990 AMC 12
- 1991 AMC 12
- 1992 AMC 12
- 1993 AMC 12
- 1994 AMC 12
- 1995 AMC 12
- 1996 AMC 12
- 1997 AMC 12
- 1998 AMC 12
- 1999 AMC 12