1969 AMC 12 Problem 27
Attempt Problem 27 of the 1969 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 1969 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
A particle moves so that its speed for the second and subsequent miles varies inversely as the integral number of miles already traveled. For each subsequent mile the speed is constant. If the second mile is traversed in hours, then the time, in hours, needed to traverse the th mile is:
Answer: E
Small hint:
During the th mile, the number of miles already traveled is
Big hint:
Time for a fixed one-mile distance varies directly as
Solution:
For the th mile, Since the distance is one mile, the time is The condition gives Therefore
Therefore, the correct answer is E.
Problem 27 in other years
- 1950 AMC 12
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