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rekhabishop
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rekhabishop
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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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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rekhabishop
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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rekhabishop
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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rekhabishop
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 time taken be t and 2t respectively for A and G = 3t
3t=27
=>t=9

let the total page written be p+2 * t + 2pt =72
solving for p we get p=2
and the no of pages of A =2+2 = 4

Therefore IMO D
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