题目
Allison always leaves her office at 5.00pm and reaches her hotel in an hour, while Brittany leaves the same hotel sometime after 5, meets Allison and reaches the same office at 6.00pm. On Wednesday, just when Brittany met Allison, she realized she had left her laptop. So she went back to the hotel, picked up her laptop and reached the office late. If Allison and Brittany always travel at constant rates, and it took Brittany exactly five minutes to retrieve her laptop between arriving at the hotel and departing again, at what time did Brittany reach the office on Wednesday?
(1) When Allison and Brittany meet each day, Allison has already covered exactly rd of the distance between the hotel and office.
(2) Brittany always leaves the hotel at exactly 5.30pm
选项
A.Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B.Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C.BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D.EACH statement ALONE is sufficient.
E.Statements (1) and (2) TOGETHER are NOT sufficient.
解析
要解决这道题，先把路线和时间可视化会有帮助：
办公室 ———————————————————— 酒店
A → ....................................................... ← B
（下午5:00出发）.............................（下午5:00之后出发）
两人都在下午6:00到达各自的目的地。这说明B比A快，因为她用更短的时间走完了相同的距离。
在B忘带笔记本电脑的那天，她遇到了A，返回酒店后又重新走了这段路。所以当天她多走的距离，是“她往常遇到A时已走距离”的两倍。
**条件1**：
已知A走了酒店和办公室之间\(\frac{2}{3}\)的距离，那么B走了剩下的\(\frac{1}{3}\)。又因为两人同时完成全程，所以相遇后，A走完了剩下的\(\frac{1}{3}\)，B走完了剩下的\(\frac{2}{3}\)。由此可推出：B的速度是A的两倍。这意味着B必须在5:30出发，才能用一半的时间完成行程（和A一样在6:00到达）。而这和条件2的信息一致，所以答案只能是D或E……
**条件2**：
B在5:30出发、6:00到达，因此她的速度是A的两倍。5:30时，A处于办公室和酒店的中点，还剩一半的路程。B会走完这“一半路程”的\(\frac{2}{3}\)（即全程的\(\frac{1}{3}\)）。所以她当天多走了\(2\times\frac{1}{3}\)的全程距离。
B走完全程需要30分钟，她走这段额外距离需要\(\frac{2}{3}\times30=20\)分钟，再加上取笔记本电脑的5分钟，她会在6:25到达办公室。
答案：(D)
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