1995 AMC 8 Problem 25
Attempt Problem 25 of the 1995 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 1995 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
Buses from Dallas to Houston leave every hour on the hour. Buses from Houston to Dallas leave every hour on the half hour. The trip from one city to the other takes hours. Assuming the buses travel on the same highway, how many Dallas-bound buses does a Houston-bound bus pass on the highway (not in the station)?
Answer: D
Small hint:
Track one Houston-bound bus over its -hour trip and see which oncoming buses share the road with it
Big hint:
Count the Dallas-bound buses already on the highway when it starts, plus those that leave before it arrives
Solution:
Consider a bus leaving Dallas at arriving in Houston at It meets every Dallas-bound bus that is on the highway during that window.
Dallas-bound buses leave Houston on the half hour and take hours. The ones sharing the road (meeting away from a station) are those that left Houston at which is buses.
Thus, the correct answer is D .
Problem 25 in other years
- 1985 AMC 8
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