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Allison and Brittany

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Allison and Brittany

by hariharanv » Sun Jun 30, 2013 5:22 pm
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, at what time did Brittany reach the office on Wednesday?

(1) Usually, when Allison and Brittany meet, Allison has already covered 2/3rd of the distance between the hotel and office.

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

P.S:
AFAIK, this Q can be solved by considering the both the statements individually. But thats not the right answer. Please explain.
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Source: — Data Sufficiency |
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by srcc25anu » Sun Jun 30, 2013 5:59 pm
Lets say distance between Office (Off) and Hotel (H) is 60 kms
Allison starts from Off at 5:00 reached hotel at 6:00 in 1 hr
therefore Allison speed = 60 m/hr

St1: WHen Allison and Brit meet, Allison has covered 2/3rd the distance. Therefore Allison has covered 40 kms
From this, we cant find at what time Brit reaches office since we dont know when Brit leaves the hotel
hence Insufficient

ST2: Brit leaves hotel at 5:30
Brit reaches office at 6:00 so it takes Brit 30 mins to cover 60 kms
Brit's speed is double Allison's speed. therefore Brit speed = 120 km/hr
Brit leaves 30 mins later than Allison starts from office. In 30 mins, Allison travels 30 kms
At 5:30, Allison and Brit are 30 kms apart and the realtive speeds is 180 km/hr
time after which the 2 meet = 30/180 = 10 mins
In 10 mins Brit covers 20 kms and Allison covers 10 kms

Now Brit returns from this point to get her laptop
therefore total time for Brit to reach office = 10 mins (from Hotel to Meeting Point) + 10 min (Meeting Point back to hotel) + 30 mins (to get back from hotel to office) = 50 mins
she started at 5:30 so she reached office at 6:20
Sufficient
Ans B
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