SOLUTION: A certain punch press requires 3h longer to stamp a box of parts than does a newer-model punch press. After the older press has been punching a box of parts for 5h , it is joined

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Question 1058783: A certain punch press requires 3h longer to stamp a box of parts than does a newer-model punch press. After the older press has been punching a box of parts for 5h , it is joined by the newer machine. Together, they finish the box of parts in 3 additional hours. How long does it take each machine, working alone, to punch a box of parts?
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The old press takes x hours alone or 1/x of the job per hour.
The new press takes x-3 hours alone or 1/(x-3) of the job per hour.
(5/x)+(3/x)+(3/x-3)=1, because the second and third terms are both punches
Multiply everything by x(x-3) to clear fractions
5(x-3)+3(x-3)+3x=x^2-3x
5x-15+3x-9+3x=x^2-3x
x^2-14x+24=0
(x-12)(x-2)=0
x=12 or 2 hours
3 can't work or the second press would take -1 hours
They are 12 hours and 9 hours respectively
(5/12)+(3/12)+(3/9) represents 8 hours by the first press and 3 hours for the second. That equals 1.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for the newer model press
to stamp box of parts
+1%2Ft+ = rate of stamping for newer model machine
+1%2F%28+t+%2B+3+%29+ = rate of stamping for older model machine
+5%2A%28+1%2F%28+t+%2B+3+%29+%29+=+5%2F%28+t+%2B+3+%29+ is the fraction of the job
the older machine does alone in 5 hrs
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The fraction of the job left is +1+-+5%2F%28+t+%2B+3+%29+
+%28%28+t+%2B+3+%29+-+5+%29+%2F+%28+t+%2B+3+%29+=+%28+t+-+2+%29+%2F+%28+t+%2B+3+%29+
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Add the rates of working for both machines to finish
+1%2Ft+%2B+1%2F%28+t%2B3+%29+=+%28+t+-+2+%29+%2F+%28+3%2A%28+t+%2B+3+%29+%29+
( note that I divided by 3 hrs to get the rate of working )
Multiply both sides by +3t%2A%28+t%2B3+%29+
+3%2A%28+t%2B3+%29+%2B+3t+=+t%2A%28+t+-+2+%29+
+3t+%2B+9+%2B+3t+=+t%5E2+-+2t+
+t%5E2+-+8t+-+9+=+0+
+%28+t+-+9+%29%2A%28+t+%2B+1+%29+=+0+ ( by inspection )
+t+=+9+ ( can only use positive solution )
+t+%2B+3+=+12+
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The older machine takes 12 hrs working alone
The newer machine takes 9 hrs working alone
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check answer:
+1%2Ft+%2B+1%2F%28+t%2B3+%29+=+%28+t+-+2+%29+%2F+%28+3%2A%28+t+%2B+3+%29+%29+
+1%2F9+%2B+1%2F12+=+7+%2F+%28+3%2A%28+9+%2B+3+%29+%29+
+1%2F9+%2B+1%2F12+=+7+%2F+36+
+4%2F36+%2B+3%2F36+=+7%2F36+
+7%2F36+=+7%2F36+
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Hope I got it -check the math