1965 AMC 12 Problem 28
Attempt Problem 28 of the 1965 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 1965 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
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:
Answer: B
Small hint:
Let ’s stepping rate be and the escalator rate be
Big hint:
Equate and
Solution:
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.
Problem 28 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
- 1966 AMC 12
- 1967 AMC 12
- 1968 AMC 12
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- 1971 AMC 12
- 1972 AMC 12
- 1973 AMC 12
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- 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