SOLUTION: hi i need help to this problem together, carmen molini and jay mccarroll can prepare a catered dinner in 20 hours. working alone, carmen can do the job 5 hours faster than jay.

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Question 136545This question is from textbook math
: hi i need help to this problem
together, carmen molini and jay mccarroll can prepare a catered dinner in 20 hours. working alone, carmen can do the job 5 hours faster than jay. find the time that each person takes to prepare a catered dinner. round to the nearest tenth.
thank you This question is from textbook math

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
together, carmen molini and jay mccarroll can prepare a catered dinner in 20 hours. working alone, carmen can do the job 5 hours faster than jay. find the time that each person takes to prepare a catered dinner. round to the nearest tenth.
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Together DATA:
Time = 20 hrs/job ; Rate = 1/20 job/hr
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Carmen DATA:
Time = x hrs/job ; Rate = 1/x job/hr
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Jay DATA:
Time = x+5 hrs/job ; Rate = 1/(x+5) job/hr
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EQUATION:
rate + rate = together rate
1/x + 1/(x+5) = 1/20
Multiply thru by 20x(x+5) to get
20(x+5) + 20x = x(x+5)
40x + 100 = x^2+5x
x^2-35x-100 = 0
x = [35 +- sqrt(35^2-4*-100)]/2
x = [35 +- sqrt(1625)]/2
x = [35 +- 40.3112]/2
x = 37.66 hrs. (Carmen's time to do the job)
x+5 = 42.66 hrs. (Jay's time to do the job)
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Cheers,
Stan H.