SOLUTION: One printer can print the paychecks for the employees of a company in 54 min. A second printer can print the checks in 81 min. How long would it take to print the checks with both

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Question 129133: One printer can print the paychecks for the employees of a company in 54 min. A second printer can print the checks in 81 min. How long would it take to print the checks with both printers operating?
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
If the first printer can print all the checks in 54 minutes, then each minute it prints
of the checks. So all you have to do is multiply this rate and you can find the
number of checks it has printed. For example, in 5 minutes this printer will print
So in 5 minutes this printer would print 5 fifty-fourths of the checks. And in t minutes this
printer will print of the checks.
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Similarly the each minute that goes by the other printer prints of the checks and
in t minutes the other printer prints of the checks.
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You can now add these two amounts of check printing together and set them equal to the 1 entire
job. So you have the equation:
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You can get rid of the denominators by first multiplying both sides of this equation (all
terms) by 54. When you multiply each term by 54 you get:
.

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Next get rid of the other denominator by multiplying both sides of this equation (all terms)
by 81 to get:
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On the left side add the two terms to get:
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And multiply out the right side to make the equation become:
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Divide both sides by 135 and you find that the equation is reduced to:
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So when both printers work together, they can complete all the payroll checks in 32.4 minutes.
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Hope this helps you to understand the problem and how to work it.
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