Answer: 30 hours
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Explanation:
Ignore the values 3000 and 1000 as they are simply labels for the printer names (or brand models). I'll call the two printers A and B for simplicity.
Printer A can produce a large document in 1/4th the time printer B can do the same job. So we can say x = (1/4)y where x and y are the times it takes for both printers to do the job if they work alone. Solving for y gets us y = 4x.
Printer A can do the full job, on its own, taking x hours. It's rate is 1/x jobs per hour. Printer B's rate is 1/y = 1/(4x) jobs per hour for similar reasons.
Their combined rate is
1/x + 1/(4x) = 4/(4x) + 1/(4x) = 5/(4x)
Set this equal to 1/6 and solve for x. The 1/6 represents the combined rate based on how they can work together to get the job done in 6 hours.
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5/(4x) = 1/6
5*6 = 4x*1 .... cross multiply
30 = 4x
4x = 30
x = 30/4 ... divide both sides by 4
x = 7.5
Printer A takes 7.5 hours to do the job alone
y = 4x
y = 4*7.5
y = 30
Printer B takes 30 hours to get the job done if it worked alone
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Note how
1/x + 1/y = 1/7.5 + 1/30 = 4/30 + 1/30 = 5/30 = 1/6
so this confirms we have the right answer.
