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Allegra and Graham edited a 72-page manuscript together, each of them

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Allegra and Graham edited a 72-page manuscript together, each of them  [#permalink]

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New post 30 Jul 2017, 03:01
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Allegra and Graham edited a 72-page manuscript together, each of them working alone at a constant rate. Graham spent twice as much time editing the manuscript as did Allegra, but Allegra edited two more pages per hour than did Graham. If the total time they spent editing the manuscript was 27 hours, how many pages did Allegra edit per hour?

A. 7
B. 6
C. 5
D. 4
E. 3

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Allegra and Graham edited a 72-page manuscript together, each of them  [#permalink]

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New post 30 Jul 2017, 03:39
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rekhabishop wrote:
Allegra and Graham edited a 72-page manuscript together, each of them working alone at a constant rate. Graham spent twice as much time editing the manuscript as did Allegra, but Allegra edited two more pages per hour than did Graham. If the total time they spent editing the manuscript was 27 hours, how many pages did Allegra edit per hour?

A. 7
B. 6
C. 5
D. 4
E. 3



Hi...

You don't have to get into substitution, the simpler way could be...
1) TIME
A does it for t hrs, so G does it for 2t hrs..
So \(t+2t=27..... t=9\)

2) PAGES
Now let G do x pages per hour, so A does x+2 pages per hour..
So \(x*18+(x+2)*9=72.....18x+9x+18=72......x=2\)

So G does 2 pages per hour and A does 2+2=4 pages per hour

D
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Re: Allegra and Graham edited a 72-page manuscript together, each of them  [#permalink]

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New post 30 Jul 2017, 03:03
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The OE suggests that we plug in values, but I want a logical explanation/approach towards this question.
OE is as below
A. No. If the total time they spent editing was 27 hours, and Graham spent twice as much time (2t) as did Allegra (t), then the total time can be written as 3t = 27. So t = 9. Thus, he spent 18 hours, and she spent 9 hours. Now plug in the answers, starting with answer choice (C). If Allegra edited 5 pages per hour, then Graham edited 3 pages per hour. Use RT = D. So Allegra edited (5)(9) = 45 pages, and Graham edited (18)(3) = 54 pages, for a total of 99 pages, which is too big. Now try something smaller, like choice (D): Allegra edited 4 pages per hour, and Graham edited 2 pages per hour. So she edited (4)(9) = 36 pages, and he edited (2)(18) = 36 pages, for a total of 72 pages, which is what you want. The correct answer is D.

B. No. If the total time they spent editing was 27 hours, and Graham spent twice as much time (2t) as did Allegra (t), then the total time can be written as 3t = 27. So t = 9. Thus, he spent 18 hours, and she spent 9 hours. Now plug in the answers, starting with answer choice (C). If Allegra edited 5 pages per hour, then Graham edited 3 pages per hour. Use RT = D. So Allegra edited (5)(9) = 45 pages, and Graham edited (18)(3) = 54 pages, for a total of 99 pages, which is too big. Now try something smaller, like choice (D): Allegra edited 4 pages per hour, and Graham edited 2 pages per hour. So she edited (4)(9) = 36 pages, and he edited (2)(18) = 36 pages, for a total of 72 pages, which is what you want. The correct answer is D.

C. No. If the total time they spent editing was 27 hours, and Graham spent twice as much time (2t) as did Allegra (t), then the total time can be written as 3t = 27. So t = 9. Thus, he spent 18 hours, and she spent 9 hours. Now plug in the answers, starting with answer choice (C). If Allegra edited 5 pages per hour, then Graham edited 3 pages per hour. Use RT = D. So Allegra edited (5)(9) = 45 pages, and Graham edited (18)(3) = 54 pages, for a total of 99 pages, which is too big. Now try something smaller, like choice (D): Allegra edited 4 pages per hour, and Graham edited 2 pages per hour. So she edited (4)(9) = 36 pages, and he edited (2)(18) = 36 pages, for a total of 72 pages, which is what you want. The correct answer is D.

D. Yes. If the total time they spent editing was 27 hours, and Graham spent twice as much time (2t) as did Allegra (t), then the total time can be written as 3t = 27. So t = 9. Thus, he spent 18 hours, and she spent 9 hours. Now plug in the answers, starting with answer choice (C). If Allegra edited 5 pages per hour, then Graham edited 3 pages per hour. Use RT = D. So Allegra edited (5)(9) = 45 pages, and Graham edited (18)(3) = 54 pages, for a total of 99 pages, which is too big. Now try something smaller, like choice (D): Allegra edited 4 pages per hour, and Graham edited 2 pages per hour. So she edited (4)(9) = 36 pages, and he edited (2)(18) = 36 pages, for a total of 72 pages, which is what you want. The correct answer is D.

E. No. If the total time they spent editing was 27 hours, and Graham spent twice as much time (2t) as did Allegra (t), then the total time can be written as 3t = 27. So t = 9. Thus, he spent 18 hours, and she spent 9 hours. Now plug in the answers, starting with answer choice (C). If Allegra edited 5 pages per hour, then Graham edited 3 pages per hour. Use RT = D. So Allegra edited (5)(9) = 45 pages, and Graham edited (18)(3) = 54 pages, for a total of 99 pages, which is too big. Now try something smaller, like choice (D): Allegra edited 4 pages per hour, and Graham edited 2 pages per hour. So she edited (4)(9) = 36 pages, and he edited (2)(18) = 36 pages, for a total of 72 pages, which is what you want. The correct answer is D.
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Re: Allegra and Graham edited a 72-page manuscript together, each of them  [#permalink]

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New post 30 Jul 2017, 06:11
chetan2u wrote:
rekhabishop wrote:
Allegra and Graham edited a 72-page manuscript together, each of them working alone at a constant rate. Graham spent twice as much time editing the manuscript as did Allegra, but Allegra edited two more pages per hour than did Graham. If the total time they spent editing the manuscript was 27 hours, how many pages did Allegra edit per hour?

A. 7
B. 6
C. 5
D. 4
E. 3



Hi...

You don't have to get into substitution, the simpler way could be...
A does it for t hrs, so G does it for 2t hrs..
So t+2t=27..... t=9

Now let G do x pages per hour, so A does x+2 pages per hour..
So x*18+(x+2)*9=72.....18x+9x+18=72......x=2

So G does 2 pages per hour and A does 2+2=4 pages per hour

D



Thanks! This was very helpful. I was doing a very silly error. :)
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Re: Allegra and Graham edited a 72-page manuscript together, each of them  [#permalink]

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New post 30 Jul 2017, 06:42
This is how I did:
Gt and At --> times taken by Graham and Allegra
Gr and Ar --> rates (Pages per hour) of Graham and Allegra
Gp and Ap --> number of pages edited by Graham and Allegra

Given,
Gp+Ap=72
Gt+At=27
Gt=2At
Ar=2+Gr

Gt+At=27 --> 2At + At=27 --> At= 9 and Gt=18
Speed= Distance/Time ==> Rate = # of pages/time
So, Ar=Ap/At, Gr=Gp/Gt
Ap= Ar*At, Gp=Gr*Gt
Ap= (2+Gr)9 ==> 18+9Gr, Gp=Gr*18

We know, Ap+Gp=72. Substitute for the values of Ap and Gp.
(18+9Gr) + 18Gr=72 ==> 27Gr= 54 or Gr=2 pages/hour

Ar= 2+Gr --> Ar=4 pages/hour

Answer: D
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Allegra and Graham edited a 72-page manuscript together, each of them  [#permalink]

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New post 30 Jul 2017, 11:41
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rekhabishop wrote:
Allegra and Graham edited a 72-page manuscript together, each of them working alone at a constant rate. Graham spent twice as much time editing the manuscript as did Allegra, but Allegra edited two more pages per hour than did Graham. If the total time they spent editing the manuscript was 27 hours, how many pages did Allegra edit per hour?

A. 7
B. 6
C. 5
D. 4
E. 3


let p=total pages edited by A
p/9-2=(72-p)/18
p=36 pages
36 pages/9 hours=4 pages per hour
D
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Allegra and Graham edited a 72-page manuscript together, each of them  [#permalink]

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New post 03 Oct 2018, 15:08
rekhabishop wrote:
Allegra and Graham edited a 72-page manuscript together, each of them working alone at a constant rate. Graham spent twice as much time editing the manuscript as did Allegra, but Allegra edited two more pages per hour than did Graham. If the total time they spent editing the manuscript was 27 hours, how many pages did Allegra edit per hour?

A. 7
B. 6
C. 5
D. 4
E. 3



Another Approach

As graham spends twice as much time editing the manuscipts than allegra, graham's efficiency/rate is half of that of algera's.
grahams rate=x
allegas rate=2x.

now given that allegra edits 2 more pages per hour than graham. so 2x-x=2;
x=2.
Allegras rate=2x=4

NOTE: you can add or subtract on efficiency/rate but not on time taken.
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Allegra and Graham edited a 72-page manuscript together, each of them   [#permalink] 03 Oct 2018, 15:08
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