SOLUTION: Kayla's copy store recived an order for 5,616 copies. The store has 3 printers. If Kayla only uses one printer at a time, the first printer would complete the job in 15 hours and 3

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Kayla's copy store recived an order for 5,616 copies. The store has 3 printers. If Kayla only uses one printer at a time, the first printer would complete the job in 15 hours and 3      Log On


   

Question 768464: Kayla's copy store recived an order for 5,616 copies. The store has 3 printers. If Kayla only uses one printer at a time, the first printer would complete the job in 15 hours and 36 minutes, the second in 7 hours and 12 minutes, and the third in 11 hours and 42 minutes. How long would it take to process if all three printers were used at the same time?
Found 2 solutions by Edwin McCravy, stanbon:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Kayla's copy store recived an order for 5,616 copies. The store has 3 printers. If Kayla only uses one printer at a time,
the first printer would complete the job in 15 hours and 36 minutes, 
That's 15·60 + 36 = 900 + 36 = 936 minutes

So the first printer's rate is 5616 copies per 936 minutes or 5616copies%2F%28936minutes%29 = 6copies%2Fminute

the second in 7 hours and 12 minutes, 
That's 7·60 + 12 = 420 + 12 = 432 minutes

So the second printer's rate is 5616 copies per 432 minutes or 5616copies%2F%28432minutes%29 = 13copies%2Fminute

and the third in 11 hours and 42 minutes. 
That's 11·60 + 42 = 660 + 42 = 702 minutes

So the third printer's rate is 5616 copies per 702 minutes or 5616copies%2F%28702minutes%29 = 8copies%2Fminute

How long would it take to process if all three printers were used at the same time?
The combined rate of all three printers is 6+13+8 or 27 copies per minute.

27 copies is to 1 minute as 5616 copies is to x minutes:

17%2F1%22%22=%22%225616%2Fx

17x = 5616
  x = 5616%2F27 = 208 minutes = 208%2F60hours = 3%2A28%2F60hours = 3 hours 28 minutes.

Edwin

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Kayla's copy store recived an order for 5,616 copies. The store has 3 printers. If Kayla only uses one printer at a time, the first printer would complete the job in 15 hours and 36 minutes, the second in 7 hours and 12 minutes, and the third in 11 hours and 42 minutes. How long would it take to process if all three printers were used at the same time?
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15 hrs and 36 min = 15.6 hrs
7 hrs and 12 min = 7.2 hrs
11 hrs ad 42 min = 11.7 hrs
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1st printer rate = 1/15.6 job/hr
2nd printer rate = 1/7.2 job/hr
3rd printer rate = 1/11.7 job/hr
together rate = 1/x job/hr
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Equation:
1/15.6 + 1/7.2 +1/11.7 = 1/x
--------
7.2*11.7x + 15.6*11.7x + 15.6*7.2x = 15.6*7.2*11.7
--------
79.2x + 182.52x + 112.32x = 1314.144
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374.04x = 1314.144
x = 3.5134 hrs = 3hrs 30.8 minutes (time to do the job together)
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Cheers,
Stan H.
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