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?

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Bella 1 week 2021-10-05T02:49:09+00:00 1 Answer 0

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    2021-10-05T02:50:23+00:00

    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

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