hapless12 wrote:

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 2/3rd of the distance between the hotel and office.

(2) Brittany always leaves the hotel at exactly 5.30pm

Official VeritasPrep solution:Solution: D. To get started on this problem, it's likely helpful to visualize the route and timing:

Office ----------------------------------------- Hotel

A --> .......................................................<-- B

(at 5:00 pm)............................................ (after 5:00 pm)

Both reach their respective destinations at 6:00 pm. This means B is faster than A since she covers the same distance in less time.

The day she forgets her laptop, she meets A, goes back to the hotel and travels the same distance again. So in all, extra distance she traveled that day is twice the distance she usually travels before she meets A.

Statement 1: Since A covers 2/3rd of the distance between hotel and office, B covers the other 1/3rd. We also know that they finish the entire journey at the same time, so after they have met A covers 1/3 of the distance and B covers 2/3 to finish the distance. So we can conclude B travels twice as quickly as A. Which means that B must have left at 5:30 to have done the same trip in half the time (finishing at 6, like A). And since this now says the same thing as statement 2, the answer must be D or E...

Statement 2: B starts at 5:30 and reaches at 6 so her speed is twice A’s speed. At 5:30, A is at the mid point between the office and hotel. Half the distance is remaining. B will cover 2/3rd of this half i.e. 1/3rd of the total distance. So she covered 2(1/3) distance extra that day. B takes 30 minutes to cover the entire distance between office and hotel. She will take (2/3)*30 = 20 mins to cover the extra distance plus the 5 minutes to retrieve the laptop, and hence will reach the office at 6:25. Answer (D)