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Question 169321This question is from textbook Introductory Algebra
: Solve the problem. The Epson Stylus 850 can print Helen's class project in 18 minutes. The Epson Stylus 500 can print the project in 36 minutes. If the two printers work together, how long would they take to print out the project?
This question is from textbook Introductory Algebra
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The Epson Stylus 850 can print Helen's class project in 18 minutes. The Epson Stylus 500 can print the project in 36 minutes. If the two printers work together, how long would they take to print out the project?
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You can shortcut this problem by noticing that 18 is half of 36. If 2 printers that each take 36 minutes work together, it's obvious that the job would take 18 minutes. So the printer that takes 18 mins can be replaced with 2 more that each take 36 minutes. Then you have 3 printers, each taking 36 minutes, so it's 36/3 = 12 minutes. See that?
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The general method:
This type of problem is the reciprocal of the sum of the reciprocals. You have to look at not the minutes per job, but the "joblets" each can do in a minute. Then you can add those up.
One printer does 1/18 of the job per minute
The other does 1/36 of the job per minute
Add them: 1/18 + 1/36 = 3/36 jobs per minute.
= 1/12 job per minute.
Invert that, = 12 minutes per job.
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This type of problem is seen in physical things often, such as 2 or more pipes filling/emptying a tank, and in electricity.
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