SOLUTION: one printer can print the paychecks for employees of a company in 54 minutes. a second printer can print the pay checks in 81 minutes. how long would it take to print the checks wi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: one printer can print the paychecks for employees of a company in 54 minutes. a second printer can print the pay checks in 81 minutes. how long would it take to print the checks wi      Log On


   

Question 876896: one printer can print the paychecks for employees of a company in 54 minutes. a second printer can print the pay checks in 81 minutes. how long would it take to print the checks with both printers operating?
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
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
%28%281%2F54%29%2A%2881%2F81%29+%2B+%281%2F81%29%2A%2854%2F54%29%29t+=+1
%28%2881%2B54%29%2F%2854%2A81%29+%29t+=+1
%28%28135%29%2F%2854%2A81%29+%29t+=+1
multiply each side by (54*81)/(135)
t+=+1+%2A+%2854%2A81%29%2F%28135%29
t+=+%2854%2A3%2A27%29%2F%285%2A27%29
t+=+%2854%2A3%29%2F%285%29
t+=+%28162%29%2F%285%29
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