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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