It takes printer A 4 more minutes than printer B to print 40 pages. If working together, the two printers can print 50 pages in 6 minutes, how long will it take printer A to print 80 pages?

It will take printer A 24 minutes to print 80 pages.

Step-by-step explanation:

It takes printer A 4 more minutes than printer B to print 40 pages.

Let the time it takes printer B be x minutes, since printer A prints at 4 minutes more, it prints at (x + 4) minutes.

Printer A prints at the rate of (40 / (x+4)) pages per minute.

Printer B prints at the rate of (40/x) pages per minute.

If working together, the two printers can print 50 pages in 6 minutes

They can print at the rate of 50 pages per 6 minutes, if working together.

Let us add these ratios, the

40 / (x + 4) + 40/x = 50/6

Divide by 40

1 / (x + 4) + 1/x = 5/24

(x + x + 4) / x (x + 4) = 5/24

2x + 4 = (5/24) (x² + 4x)

48x + 96 = 5x² + 20x

5x² - 28x - 96 = 0

Solving this using the quadratic formula,

x = [-b ± √ (b² - 4ac) ]/2a

a = 5, b = - 28, and c = - 96

x = [28 ± √ (784 + 1920) ]/10

= 28/10 ± √ (2704) / 10

= 28/10 ± 52/10

x = (28+52) / 10 = 80/10 = 8

Or

x = (28 - 52) / 10 = - 24/10 = - 2.4

So, x is either 8 or - 2.4

Since we are dealing with time, the realistic value is the positive value, x = 8, then we choose x = 8 minutes.

It takes printer A (x + 4) minutes to print 40 pages.

x + 4 = 12 minutes.

So, it takes it 12 minutes to print 40 pages.

Easily, it will take it twice as much time to print 80 pages.

So, it will take it 24 minutes to print 80 pages.