It takes an hp printer 12 minutes longer to complete a 576 page print job by itself than it takes a canon printer to complete the same job by itself. Together the two printers can complete the job in 8 minutes. How long does it take each printer to complete the print job alone?. How many pages per minute does each printer print?

Part A: The Canon printer will complete the print job alone in 12 minutes and the HP Printer in 24 minutes.

Part B: The Canon printer prints 48 pages per minute, meanwhile the HP Printer prints 24 pages per minute.

Step-by-step explanation:

Let's recall that a problem involving combined work can be solved using the formula:

T/A + T/B = 1, where:

T = time the printers working together

A = the time for the Canon printer working alone

B = the time for the HP printer working alone

How long does it take each printer to complete the print job alone?

To solve for T, A and B, we have that:

T = 8 minutes

A = x

B = x + 12

Therefore,

8/x + 8 / (x + 12) = 1

8 (x + 12) + 8x = x * (x + 12) (Lowest Common Denominator is x * (x + 12)

8x + 96 + 8x = x² + 12x

- x² + 4x + 96 = 0

x² - 4x - 96 = 0

(x - 12) * (x + 8) = 0

x₁ - 12 = 0

x₂ + 8 = 0

x₁ = 12

x₂ = - 8

We discard x₂ because time could not be a negative value and just take x₁

A = 12 ⇒ B = 24

How many pages per minute does each printer print?

The print job is to complete 576 pages, in consequence:

Canon printer = 576/12 = 48 pages per minute

HP Printer = 576/24 = 24 pages per minute