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# Allison always leaves her office at 5.00pm and reaches her

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Joined: 18 Feb 2014
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Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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Updated on: 03 Jun 2014, 09:20
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Difficulty:

95% (hard)

Question Stats:

31% (02:29) correct 69% (02:41) wrong based on 316 sessions

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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

Originally posted by hapless12 on 03 Jun 2014, 05:08.
Last edited by Bunuel on 03 Jun 2014, 09:20, edited 3 times in total.
RENAMED THE TOPIC.
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Re: Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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03 Jun 2014, 06:10
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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.

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Joined: 13 Sep 2015
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Re: Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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20 Oct 2015, 08:05
1
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

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Re: Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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02 Mar 2017, 20:45
1
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)
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Re: Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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03 Mar 2017, 04:26
Its D..
clue is: Britney take same time to cover 2/3D as Allison take 1/3D to cover...we will get relation for speed and we can deduce time it take Britney to complete he journey ...

Best part of the solution : A will give same info as B ...So if A is Suff , B will be ....
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Joined: 27 Dec 2015
Posts: 11
Re: Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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03 Nov 2017, 06:03
Nowhere is it mentioned for how long these people meet, so shouldn't we be taking this into account as well?
Math Expert
Joined: 02 Sep 2009
Posts: 52902
Re: Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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03 Nov 2017, 06:06
rohitsatya wrote:
Nowhere is it mentioned for how long these people meet, so shouldn't we be taking this into account as well?

"Meet" here does not mean that they meet to chat. "Meet", here means that they pass each other.
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Posts: 240
Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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Updated on: 02 Apr 2018, 08:31
Does in an hour mean "exactly one hour" or "somewhat less than one hour"?

Thanks
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We Shall Overcome... One day...

Originally posted by nahid78 on 02 Apr 2018, 07:47.
Last edited by nahid78 on 02 Apr 2018, 08:31, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 52902
Re: Allison always leaves her office at 5.00pm and reaches her  [#permalink]

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02 Apr 2018, 07:50
1
nahid78 wrote:
Does in an hour means "exactly one hour" or "somewhat less than one hour"?

Thanks

"Allison ... reaches her hotel in an hour" means that Allison needs exactly 1 hour to reach the hotel.
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Re: Allison always leaves her office at 5.00pm and reaches her   [#permalink] 02 Apr 2018, 07:50
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