Question 876896
Printer 1 , 1 paycheck run per 54 minutes
The rate is ( 1/54 paycheck run )/ minute
Printer 2 , 1 paycheck run per 81 minutes
The rate is ( 1/81 paycheck run )/ minute
Set t = time to complete the paycheck run
(1/54)t + (1/81)t = 1 paycheck run
(1/54 + 1/81)t = 1
{{{((1/54)*(81/81) + (1/81)*(54/54))t = 1}}}
{{{((81+54)/(54*81) )t = 1}}}
{{{((135)/(54*81) )t = 1}}}
multiply each side by (54*81)/(135)
 {{{t = 1 * (54*81)/(135)}}}
 {{{t = (54*3*27)/(5*27)}}}
 {{{t = (54*3)/(5)}}}
 {{{t = (162)/(5)}}}
Let's verify substituting 162/5 for t  in (1/54 + 1/81)t = 1
(1/54 + 1/81)(162/5) = 1
This does check out, see
http://www.wolframalpha.com/input/?i=%281%2F54+%2B+1%2F81%29%28162%2F5%29
So the time is 162/5 = 32.4 minutes