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answers:
roderick_young say: Normal way to do it in algebra:

portion of an essay that Donna can do in a minute: 1/4
portion of an essay that Clay can do in a minute: 1/6
given m minutes, how many essays can they do together:
m * 1/4 + m * 1/6 = m(1/4 + 1/6)
set that equal to the number of essays desired, and solve for minutes:
m(1/4 + 1/6) = 20

if the answer does not come out that each person did a whole number of essays, then you will need to solve for the boundary case, looking at who will finish their essay first

fast way for competitions:

For every 3 essays Donna does, Clay does 2 (taking 12 minutes in the process). So they take 12 minutes to do 5. Scaling up, 48 minutes to do 20.

even faster way:

recognize that it's multiple choice, and the choices are far apart. Two Clays would take 3 mins per essay, which would be 60 minutes for 20. Two Donnas would take 2 minutes per essay, so 40 minutes. So the answer must be between 40 and 60.
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Como say: Average time for 1 essay is 5 mins
Time for 20 essays 100 mins_____Option D
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RR say: Donna takes 4 minutes, so in 6 minutes she has graded 1.5 esays.

After 6 minutes, Donna will have graded 1.5 essays and Clay will have graded 1.
Together, they will have graded 1.5 + 1 = 2.5 essays

20 essays divided by 2.5:

20/2.5 = 8.

That means there are 8 lots of 2.5 essays

Therefore it takes 8 x 6 minutes = 48 minutes.
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JG say: Work = rate * time
Donna completes 1/4 essay in one minute and Clay completes 1/6 in one minute
Combined rate = 1/4+1/6 = 10/24 = 5/12 essays/minute
Time to complete 20 essays = 20 essays/(5/12 essays/minute) = 20 * 12/5 minutes = 48 minutes.

The answer is B.
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Krishnamurthy say: B.48
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ted s say: comment : in 12 minutes they grade 5
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Ian H say: Combined rate is 1/4 + 1/6 = 5/12 essays per minute
20 essays take 20*12/5 = 48 mins
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az_lender say: In 12 minutes, Donna grades 3 and Clay grades 2, for a total of 5 (between the two graders). So it takes 48 minutes for the two of them to grade 20 essays, if they don't stop for coffee or whatever.
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rotchm say: Many ways to do this. Here is a hint :

In 12 mins, donna does how many? & clay? Thus, together in 12 mins they do how many?

Thus how much time to do 20 essays ?

Hopefully no one will spoil you the answer thereby depriving you from your personal enhancement; that would be very inconsiderate of them.
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blah say: stop being lazy
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Mr. Un-couth say: Answer = 48 minutes.

With both Donna and Clay both grading a total of 20 essays for the same amount of time and because of Donna's quickness she can do (6/10) of the 20 essays or 12 essays and Clay can only do (4/10) of the 20 essays or 8 essays during the same time Donna was grading 12 essays.
Total minutes required = [(12 essays)@(4 min/essay)] or since they are both grading essays at the same time [(8 essays)@(6 min/essay)] = (48)min
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sepia say: It takes Donna 4 minutes for 1 essay and Clay 6 minutes for 1.
If both start grading @ same time,
20 essays can be graded in 48 minutes.
Answer
B. 48 minutes
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qknxk say: avyfcqvb
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