SOLUTION: One watering system needs about 3 times as long to complete a job as another watering system. When both systems operate at the same time, the job can be completed in 9 minutes. How

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Question 120245This question is from textbook Prentice Hall Algebra 1
: One watering system needs about 3 times as long to complete a job as another watering system. When both systems operate at the same time, the job can be completed in 9 minutes. How long does it take each system to do the job alone?
Thanks.
EliThis question is from textbook Prentice Hall Algebra 1

Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
One watering system needs about 3 times as long to complete a job as another watering system. When both systems operate at the same time, the job can be completed in 9 minutes. How long does it take each system to do the job alone?
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1st system DATA:
Time = 3x minutes/job ; Rate = 1/(3x) job/min
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2nd system DATA:
Time = x minutes/job ; Rate = 1/x job/min
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Together DATA:
Time = 9 min/job ; Rate = 1/9 job/min
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EQUATION:
rate + rate = together rate
1/(3x) + 1/x = 1/9
Multiply thru by 27x to get:
9 + 27 = 3x
36 = 3x
x = 12 min (time for 2nd system to do the job alone)
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3x = 36 min (time for the 1st system to do the job alone)
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Cheers,
Stan H.