1995 AMC 8 第 25 题

先试着解答 1995 AMC 8 第 25 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1995 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

25.

从达拉斯到休斯敦的巴士每小时整点发车。从休斯敦到达拉斯的巴士每小时半点发车。两城之间的行程需要 55 小时。假设巴士都在同一条公路上行驶,一辆开往休斯敦的巴士会在公路上(不在车站内)遇到多少辆开往达拉斯的巴士?
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 55 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)?
55
66
99
1010
1111
答案:D
知识点:路程、速度与时间
小提示:
跟踪一辆开往休斯敦的巴士在 55 小时行程中,会与哪些迎面巴士同时在路上
Track one Houston-bound bus over its 55-hour trip and see which oncoming buses share the road with it
大提示:
数它出发时已经在公路上的开往达拉斯的巴士,加上它到达前出发的那些
Count the Dallas-bound buses already on the highway when it starts, plus those that leave before it arrives
解答:
考虑一辆 6 ⁣: ⁣006\!:\!00 从达拉斯出发、11 ⁣: ⁣0011\!:\!00 到休斯敦的巴士。它会遇到所有在这段时间内与它同在公路上的开往达拉斯的巴士。
开往达拉斯的巴士每半点从休斯敦出发,行程 55 小时。与这辆车在路上相遇且不在车站相遇的,是 1 ⁣: ⁣301\!:\!30、2 ⁣: ⁣302\!:\!30、…\ldots、10 ⁣: ⁣3010\!:\!30 从休斯敦出发的巴士,共 1010 辆。
所以正确答案是 D。
Consider a bus leaving Dallas at 6 ⁣: ⁣00,6\!:\!00, arriving in Houston at 11 ⁣: ⁣00.11\!:\!00. 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 55 hours. The ones sharing the road (meeting away from a station) are those that left Houston at 1 ⁣: ⁣30,1\!:\!30, 2 ⁣: ⁣30,2\!:\!30, …,\ldots, 10 ⁣: ⁣30,10\!:\!30, which is 1010 buses.
Thus, the correct answer is D .
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