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 183453: 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 produce this number of pages?
Answer by josmiceli(6786) About Me  (Show Source):
You can put this solution on YOUR website!
Call the certain number of pages 1 job
Call the 1st machine's rate of printing pages r
Then the 2nd machines rate is r%2F2
Working together, their combined rate is 1%2F8
which is 1 job in 8 minutes
I can add the 2 rates to get the combined rate
r+%2B+r%2F2+=+1%2F8
8r+%2B+4r+=+1
12r+=+1
r+=+1%2F12
This means the 1st machine, working alone,
can print the pages in 12 minutes
r%2F2+=+%281%2F12%29%2F2
r%2F2+=+1%2F24
This means the 2nd machine, working alone,
can print the pages in 24 minutes
check answer:
r+%2B+r%2F2+=+1%2F8
1%2F12+%2B+1%2F24+=+1%2F8
Multiply both sides by 24
2+%2B+1+=+3
3+=+3
OK