## 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 b

Question

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?

in progress
0

Math
1 week
2021-10-05T02:49:09+00:00
2021-10-05T02:49:09+00:00 1 Answer
0
## Answers ( )

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 x₁A = 12 ⇒ B = 24How 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 minuteHP Printer = 576/24 = 24 pages per minute