Bunuel 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
Make a table, reduce time by common denominator 3
___r___t__W
X 1/4__4__1
Y 1/5__5__1
Z 1/6__6__1
We are asked to find time X / time (Y+Z); use 1/rate(Y+Z) to express time:
\(\frac{4}{( 1 / (1/5+1/6)}\)
\(\frac{4}{( 1 / (11/30)}\)
\(\frac{4}{(30/11)}\)
\(\frac{4*11}{30}\)
\(\frac{22}{15}\)