SOLUTION: it takes two laser printers 108 minutes, working together to complete 5760 page print job. if each printer is printing this job alone, the first laser printer takes 90 minutes long

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Question 460750: it takes two laser printers 108 minutes, working together to complete 5760 page print job. if each printer is printing this job alone, the first laser printer takes 90 minutes longer than the second laser printer.
How long does it take each printer to print the job alone? What is the speed of each printer?
It takes the second printer ? number of minutes to complete the job alone.
It takes the first printer ? number of minutes to complete the job alone.
The speed of the second printer is ? number of pages per minute.
The speed of the first printer is ? number of pages per minute
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
it takes two laser printers 108 minutes, working together to complete 5760 page print job. if each printer is printing this job alone, the first laser printer takes 90 minutes longer than the second laser printer.
How long does it take each printer to print the job alone? What is the speed of each printer?
It takes the second printer ? number of minutes to complete the job alone.
It takes the first printer ? number of minutes to complete the job alone.
The speed of the second printer is ? number of pages per minute.
The speed of the first printer is ? number of pages per minute
..
let x=minutes second printer takes to complete the job alone
1/x=second printer work rate
x+90=minutes first printer takes to complete the job alone
1/(x+90)=first printer work rate
108 minutes to complete the job when working together
1/108 =work rate when working together
..
sum of individual work rates=work rate when working together
1/x+1/(x+90)=1/108
LCD:x(x+90)(108)
108x+90*108+108x=x^2+90x
216x+9720=x^2+90x
x^2-126x-9720=0
use quadratic formula to solve
a=1, b=-126, c=-9720
x=[-(-126)ħsqrt((-126)^2-4*1*-9720)]2*1
x=[126ħsqrt(54756)]2
x=[126ħ234]/2
x=-54 (reject, x>0)
or
x=180 minutes
ans:
It takes second printer 180 minutes to complete the job alone
It takes first printer 180+90=270 minutes to complete the job alone
The speed of the second printer is 5760/180= 32 pages per minute.
The speed of the first printer is 5760/270= 21.33 pages per minute.
The speed of 2 printers working together is 5760/108= 53.33 pages per minute.