Expert: Sherman D. - 5/6/2009

Question
Working alone, printers X,Y,and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hrs, respetively.What is the ratio of the time it takes printer Y and Z to do the job, working together at their individual rates?

Answer
X and Y together
(1/12) + (1/15) = (1/t)
(5/60) + (4/60) = (1/t)
(9/60) = (1/t)
t = (20/3) or 6 hours and 40 minutes

X and Z together
(1/12) + (1/18) = (1/t)
(3/36) + (2/36) = (1/t)
(5/36) = (1/t)
t = (36/5) or 7 hours and 12 minutes

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Y and Z together
(1/15) + (1/18) = (1/t)
(6/90) + (5/90) + (1/t)
(11/90) = (1/t)
t = (90/11) or 8 hours and 10 minutes and 55 seconds

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now if all 3 of them worked together
(1/12) + (1/15) + (1/18) = (1/t)
(45/540) + (36/540) + (30/540) = (1/t)
(111/540) = (1/t)
t = (540/111) or about 4 hours and 52 minutes

the others were just extra information in case you have another problem like it.