It takes printer A 4 more minutes than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take printer A to print 80 pages?
* 12
* 18
* 20
* 24
* 30
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It takes printer B x minutes to print 40 pages and 5x/4 minutes to print 50 pages.
It takes printer A x+4 minutes to print 40 pages and 5/4x+5 minutes to print 50 pages.
1/A+1/B=1/6
A=The time it takes A alone to print 50 pages.
B= The time it takes B alone to print 50 pages.
4/(5x+20)+4/(5x)=1/6
20x+20x+80/(25x^2+100x)=1/6
6(40x+80)=25x^2+100x
240x+480=25x^2+100x
25x^2-140x-480=0
Divide by 5.
5x^2-28x-96=0
Quadratic formula:
-b+/-sqrt(b^2-4ac)/2a
x=28+/-sqrt(28^2-20(-96))/10
x=8
Disregard the negative value that you get from the formula.
This means that Printer A can print 40 pages in 8+4 or 12 mins and 80 pages in 12*2 or 24 mins.
D
It takes printer A x+4 minutes to print 40 pages and 5/4x+5 minutes to print 50 pages.
1/A+1/B=1/6
A=The time it takes A alone to print 50 pages.
B= The time it takes B alone to print 50 pages.
4/(5x+20)+4/(5x)=1/6
20x+20x+80/(25x^2+100x)=1/6
6(40x+80)=25x^2+100x
240x+480=25x^2+100x
25x^2-140x-480=0
Divide by 5.
5x^2-28x-96=0
Quadratic formula:
-b+/-sqrt(b^2-4ac)/2a
x=28+/-sqrt(28^2-20(-96))/10
x=8
Disregard the negative value that you get from the formula.
This means that Printer A can print 40 pages in 8+4 or 12 mins and 80 pages in 12*2 or 24 mins.
D
