SOLUTION: One machine in a print shop can produce a certain number of pages twice as fast as another machine. Operating together, these machines can produce this number of pages in 8 minutes

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Question 33672This question is from textbook Algebra 1
: One machine in a print shop can produce a certain number of pages twice as fast as another machine. Operating together, these machines can produce this number of pages in 8 minutes. How long would it take each machine, working alone, to producing this number of pages? This question is from textbook Algebra 1

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
One machine = 2x
Other machine = x
Equation:
1%2F2x%2B1%2Fx=1%2F8 or 1%2F2x%2B1%2Fx=0.125
(2x+x)=0.125[(2x)(x)]
3x=0.25x^2
0.25x^2-3x=0
times the equation by 4:
x^2-12x=0
Differentate with respect to x
dy%2Fdt=%282x%29dx%2Fdt-%2812%29%2Fdx%2Fdt
-2x=-12
x=6
Mutliply the results by 2:
2(6)=12
Hence, one machine can produce 12 pages and other can produce 2(12)=24 pages.
Paul.