1970 AMC 12 第 29 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。
29.
现在是 至 之间。六分钟后，手表的分针将恰好指向三分钟前时针所指位置的正对面。现在的准确时间是多少？
It is now between and o’clock, and six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now?
小提示：
设现在是 之后 分钟
Let be the number of minutes after now
大提示：
以分钟刻度为单位，未来的分针位于 ，而过去时针位置的对面位于
In minute-space units, the future minute hand is at , while the point opposite the past hour hand is at
解答：
设现在是 之后 分钟。六分钟后，分针从 顺时针走过 个分钟刻度。三分钟前，时针越过 的位置 个分钟刻度，所以它的正对面位于 即从 起经过这么多个分钟刻度。因此 解得 ，所以时间是 。
因此，正确答案是 D。
Let be the number of minutes after now. Six minutes from now, the minute hand is minute spaces clockwise from Three minutes ago, the hour hand was minute spaces past the so the point opposite it was minute spaces past Hence Solving gives so the time is
Therefore, the correct answer is D.
其他年份的第 29 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
- 1967 AMC 12
- 1968 AMC 12
- 1969 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
- 1981 AMC 12
- 1982 AMC 12
- 1983 AMC 12
- 1984 AMC 12
- 1985 AMC 12
- 1986 AMC 12
- 1987 AMC 12
- 1988 AMC 12
- 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