Roland2rule 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
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 job
Example: 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 job
Example: 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.
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 hour
Printer Z takes 18 hours to complete a job. So, by rule #1, printer Z's rate is 1/18 of the job
per hour
So, their combined rate per hour = 1/15 + 1/18
= 6/90 + 5/90
=
11/90
So, 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)
= [spoiler]22/15[/spoiler]
=
D
Cheers,
Brent
