SOLUTION: Machine A turns out 500 buttons in a certain number of minutes and Machine B turns out the same number of buttons in twice the time of Machine A. When both machines are used to pro

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Question 132277: Machine A turns out 500 buttons in a certain number of minutes and Machine B turns out the same number of buttons in twice the time of Machine A. When both machines are used to produce 500 buttons, the time required is 40 minutes. Find the number of minutes each machine turns out 500 buttons.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Since the problem only talks about 500 buttons and no other number
of buttons, I can call 500 buttons 1 job
(machine A's rate) + (machine B's rate) = (rate running together)
(1 job / x minutes) + (1 job / 2x minutes) = 1 job / 40 minutes)
1%2Fx+%2B+1%2F%282x%29+=+1%2F40
Multiply both sides by 2%2Ax%2A40
80+%2B+40+=+2x
2x+=+120
x+=+60
Machine A makes 500 buttons in 60 minutes
Machine B makes 500 buttons in 120 minutes
check:
1%2Fx+%2B+1%2F%282x%29+=+1%2F40
1%2F60+%2B+1%2F120+=+1%2F40
2%2F120+%2B+1%2F120+=+3%2F120
1+%2B+2+=+3
OK