Carcass wrote:

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 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11

(B) 1/2

(C) 15/22

(D) 22/15

(E) 11/4

----ASIDE-----------------------------------

For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the jobExample: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire jobExample: If Sam can complete 1/8 of the job

in one hour, then it will take him 8/1 hours to complete the job.

Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

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Let’s use these rules to solve the question. . . .

Printer Y takes 15 hours to complete a job. So, by rule #1, printer Y’s rate is 1/15 of the job

per hourPrinter Z takes 18 hours to complete a job. So, by rule #1, printer Z’s rate is 1/18 of the job

per hourSo, their combined rate per hour = 1/15 + 1/18

= 6/90 + 5/90

=

11/90So, working together, printers Y and Z can complete the

11/90 of the job

in one hour.

When we apply rule #2, we can conclude that, working together, printers Y and Z will complete the entire job in

90/11 hours.

What is the ratio of the time it takes printer X to do the job, working at its rate, to time it takes printers y and z to do the job?So, (time for X to complete)/ (time for Y & Z to complete) = 12/(

90/11)

= (12)(11/90)

= 22/15

Answer: D

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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