2014 AMC 8 Problem 25
Attempt Problem 25 of the 2014 AMC 8 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 2014 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
A straight one-mile stretch of highway, feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at miles per hour, how many hours will it take to cover the one-mile stretch?
Note: mile = feet
Answer: B
Small hint:
Each semicircle advances Robert feet along the highway.
Big hint:
Compare the length of a semicircle to its diameter.
Solution:
Each semicircle advances Robert feet along the highway, so a one-mile stretch requires semicircles.
Each semicircle has diameter feet, so its arc length is feet. The total distance Robert rides is feet, which is miles.
At miles per hour, the time is hours.
Thus, B is the correct answer.
Problem 25 in other years
- 1985 AMC 8
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