document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #529044 by LinnW(1048) $\"\"$ $\"About$

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Printer 1 , 1 paycheck run per 54 minutes
\n" ); document.write( "The rate is ( 1/54 paycheck run )/ minute
\n" ); document.write( "Printer 2 , 1 paycheck run per 81 minutes
\n" ); document.write( "The rate is ( 1/81 paycheck run )/ minute
\n" ); document.write( "Set t = time to complete the paycheck run
\n" ); document.write( "(1/54)t + (1/81)t = 1 paycheck run
\n" ); document.write( "(1/54 + 1/81)t = 1
\n" ); document.write( " $\"%28%281%2F54%29%2A%2881%2F81%29+%2B+%281%2F81%29%2A%2854%2F54%29%29t+=+1\"$
\n" ); document.write( " $\"%28%2881%2B54%29%2F%2854%2A81%29+%29t+=+1\"$
\n" ); document.write( " $\"%28%28135%29%2F%2854%2A81%29+%29t+=+1\"$
\n" ); document.write( "multiply each side by (54*81)/(135)
\n" ); document.write( " $\"t+=+1+%2A+%2854%2A81%29%2F%28135%29\"$
\n" ); document.write( " $\"t+=+%2854%2A3%2A27%29%2F%285%2A27%29\"$
\n" ); document.write( " $\"t+=+%2854%2A3%29%2F%285%29\"$
\n" ); document.write( " $\"t+=+%28162%29%2F%285%29\"$
\n" ); document.write( "Let's verify substituting 162/5 for t in (1/54 + 1/81)t = 1
\n" ); document.write( "(1/54 + 1/81)(162/5) = 1
\n" ); document.write( "This does check out, see
\n" ); document.write( "http://www.wolframalpha.com/input/?i=%281%2F54+%2B+1%2F81%29%28162%2F5%29
\n" ); document.write( "So the time is 162/5 = 32.4 minutes \n" ); document.write( "

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