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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
(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
03 Jun 2014, 07:10
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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?
{Office}------------|----(meeting point)--------{Hotel}
(Allison -->)--------------------------------(<-- Brittany )
(1) When Allison and Brittany meet each day, Allison has already covered exactly 2/3rd of the distance between the hotel and office.
2/3rd of the distance requires 2/3rd of the time, so 2/3 hours. This implies that they meet at 5:40pm. Since Brittany usually reaches the office at 6.00pm, then she usually needs 1/3 hours (20 minute) to cover 2/3rd of the distance (after the meeting point). To cover 1/3rd of the distance she needs 1/6 hours = 10 minutes. Therefore she left at 5:40 - 10 minutes = 5:30pm.
The total distance covered by Brittany on Wednesday is {1/3rd of the distance} (to the meeting point) + {1/3rd of the distance} (back to the hotel) + {whole distance}, thus he needs (10 minutes) + (10 minutes) + (30 minutes) + (5 minutes to retrieve her laptop) = 55 minutes from 5:30pm. Sufficient.
(2) Brittany always leaves the hotel at exactly 5.30pm.
Allison covers the distance from office to hotel in 1 hour --> her rate = d/1 = d miles per hour.
Brittany covers the distance from hotel to office in 1/2 hour --> her rate = d/(1/2) = 2d miles per hour.
In half an hour, from 5.00pm to 5.30pm, Alisson covers (time)(rate) = 1/2*d =d/2 miles.
The remaining d/2 miles, before their meeting, will be split into 1 to 2 ratio (since Brittany's speed is twice of that of Allison's, she covers twice as much distance as Brittany). Thus, Brittany will cover d/2*2/3=d/3 miles before they meet.
Therefore, the total distance covered by Brittany on Wednesday is d/3 (to the meeting point) + d/3 (back to the hotel) + d = 5d/3 miles. To cover 5d/3 miles, she needs (5d/3)/(2d) = 5/6 hours. Thus, Brittany reached office at 5.30pm + (5/6 hours) + (5 minutes to retrieve her laptop). Sufficient.
Answer: D.
{Office}------------|----(meeting point)--------{Hotel}
(Allison -->)--------------------------------(<-- Brittany )
(1) When Allison and Brittany meet each day, Allison has already covered exactly 2/3rd of the distance between the hotel and office.
2/3rd of the distance requires 2/3rd of the time, so 2/3 hours. This implies that they meet at 5:40pm. Since Brittany usually reaches the office at 6.00pm, then she usually needs 1/3 hours (20 minute) to cover 2/3rd of the distance (after the meeting point). To cover 1/3rd of the distance she needs 1/6 hours = 10 minutes. Therefore she left at 5:40 - 10 minutes = 5:30pm.
The total distance covered by Brittany on Wednesday is {1/3rd of the distance} (to the meeting point) + {1/3rd of the distance} (back to the hotel) + {whole distance}, thus he needs (10 minutes) + (10 minutes) + (30 minutes) + (5 minutes to retrieve her laptop) = 55 minutes from 5:30pm. Sufficient.
(2) Brittany always leaves the hotel at exactly 5.30pm.
Allison covers the distance from office to hotel in 1 hour --> her rate = d/1 = d miles per hour.
Brittany covers the distance from hotel to office in 1/2 hour --> her rate = d/(1/2) = 2d miles per hour.
In half an hour, from 5.00pm to 5.30pm, Alisson covers (time)(rate) = 1/2*d =d/2 miles.
The remaining d/2 miles, before their meeting, will be split into 1 to 2 ratio (since Brittany's speed is twice of that of Allison's, she covers twice as much distance as Brittany). Thus, Brittany will cover d/2*2/3=d/3 miles before they meet.
Therefore, the total distance covered by Brittany on Wednesday is d/3 (to the meeting point) + d/3 (back to the hotel) + d = 5d/3 miles. To cover 5d/3 miles, she needs (5d/3)/(2d) = 5/6 hours. Thus, Brittany reached office at 5.30pm + (5/6 hours) + (5 minutes to retrieve her laptop). Sufficient.
Answer: D.
General Discussion
20 Oct 2015, 09:05
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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
To solve this question lets determine the information given :-
5:00 Allison leaves office------------=---------6:00 Allison reaches hotel
Allison & Britt meet
5:something Brittany leaves hotel---=-------- 6:00 Brittany reaches office
Time taken to retrieve laptop - 5 mins
Statement 1 - Allison covers 2/3rd when she meets Britt
Since Allison covers entire distance in 1hr, she covers 2/3 distance in 40 mins. Therefore she meets Brittany at 5:40
Since Allison has covered 2/3rd the distance, Brittany must have travelled 1/3rd the distance to meet at the same point. Since Brittany reaches office at 6, she must be covering the remaining 2/3rd distance in 20 mins, therefore she must have already travelled for 10 mins.
Thus, time Brittany will reach office on Wed = 5:40 + return back 1/3rd distance + time to retreive laptop + entire distance
= 5:40 + 10 +5+ 30
=6:25 Sufficient
Statement 2- Brittany leaves hotel at 5:30, therefore on normal days she covers entire distance in 30 mins as she reaches office by 6:00pm. Allison on the other hand must have travelled for half hour and covered half the distance by the time Brittany begins her journey.
Therefore it follows ratio of speed of britt:allison = 2:1, ratio of time (inversely proportional) = 1:2,
Allison has to cover 1/2 distance to reach hotel at 6:00, thus Allison and Brittany will cover 1/2d remaining in the ratio 2:1
before they meet. Therefore Allison would cover 1/3*1/2d and Brittany would cover 2/3*1/2d
Basis the above information we can calculate the total distance Brittany has to travel on Wednesday
2(2/3*1/2d) + d + Additional 5 mins to retrieve her laptop
2/3d + d + add 5 mins
We know that on normal days Brittany takes 30 mins to cover distance d
Therefore time at which she will reach on Wednesday = 5:30 + 20 (2/3d) + 30 (d) + 5 (time taken to retrieve)
=6:25 Sufficient
Answer : D
(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
To solve this question lets determine the information given :-
5:00 Allison leaves office------------=---------6:00 Allison reaches hotel
Allison & Britt meet
5:something Brittany leaves hotel---=-------- 6:00 Brittany reaches office
Time taken to retrieve laptop - 5 mins
Statement 1 - Allison covers 2/3rd when she meets Britt
Since Allison covers entire distance in 1hr, she covers 2/3 distance in 40 mins. Therefore she meets Brittany at 5:40
Since Allison has covered 2/3rd the distance, Brittany must have travelled 1/3rd the distance to meet at the same point. Since Brittany reaches office at 6, she must be covering the remaining 2/3rd distance in 20 mins, therefore she must have already travelled for 10 mins.
Thus, time Brittany will reach office on Wed = 5:40 + return back 1/3rd distance + time to retreive laptop + entire distance
= 5:40 + 10 +5+ 30
=6:25 Sufficient
Statement 2- Brittany leaves hotel at 5:30, therefore on normal days she covers entire distance in 30 mins as she reaches office by 6:00pm. Allison on the other hand must have travelled for half hour and covered half the distance by the time Brittany begins her journey.
Therefore it follows ratio of speed of britt:allison = 2:1, ratio of time (inversely proportional) = 1:2,
Allison has to cover 1/2 distance to reach hotel at 6:00, thus Allison and Brittany will cover 1/2d remaining in the ratio 2:1
before they meet. Therefore Allison would cover 1/3*1/2d and Brittany would cover 2/3*1/2d
Basis the above information we can calculate the total distance Brittany has to travel on Wednesday
2(2/3*1/2d) + d + Additional 5 mins to retrieve her laptop
2/3d + d + add 5 mins
We know that on normal days Brittany takes 30 mins to cover distance d
Therefore time at which she will reach on Wednesday = 5:30 + 20 (2/3d) + 30 (d) + 5 (time taken to retrieve)
=6:25 Sufficient
Answer : D
