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

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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)   (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



multiply each side by (54*81)/(135)




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
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