1965 AMC 12 第 28 题
先试着解答 1965 AMC 12 第 28 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1965 AMC 12 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
28.
一部向下匀速运行的自动扶梯始终可见 级等高台阶。两个男孩 和 随扶梯稳定向下走， 每分钟走过的扶梯台阶数是 的两倍。 走了 步到达底端，而 走了 步到达底端。则 为：
An escalator (moving staircase) of uniform steps visible at all times descends at constant speed. Two boys, and walk down the escalator steadily as it moves, negotiating twice as many escalator steps per minute as reaches the bottom after taking steps while reaches the bottom after taking steps. Then is:
小提示：
设 的步速为 ，扶梯速度为
Let ’s stepping rate be and the escalator rate be
大提示：
令 与 相等
Equate and
解答：
设 每分钟走 步，则 每分钟走 步，并设扶梯每分钟贡献 级台阶。他们的行进时间分别为 和 。因此 解得 ，从而 。
因此，正确答案是 B。
Let take steps per minute, so takes and let the escalator contribute steps per minute. Their travel times are and Thus This gives and then
Therefore, the correct answer is B.
其他年份的第 28 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
- 1966 AMC 12
- 1967 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
- 1981 AMC 12
- 1982 AMC 12
- 1983 AMC 12
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- 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