Answer:
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
