1964 AMC 12 Problem 26
Attempt Problem 26 of the 1964 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 1964 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
In a ten-mile race First beats Second by miles and First beats Third by miles. If the runners maintain constant speeds throughout the race, by how many miles does Second beat Third?
Answer: C
Small hint:
When First finishes, Second and Third have run and miles
Big hint:
Compare Third’s distance when Second completes miles
Solution:
Relative to First’s speed, Second’s speed is and Third’s is Thus Third runs as fast as Second. When Second finishes miles, Third has run miles, so Second wins by miles.
Therefore, the correct answer is C.
Problem 26 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
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