Question 109280: two pipes togather can fill a large tank in 10hrs. one of the pipes , used alone , takes 15hrs longer than the other to fill the tank . hown long would each pipe take to fill the tank alone?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! two pipes togeather can fill a large tank in 10hrs
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Together DATA:
Time = 10 hrs/job ; Rate = 1/10 job/hr
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one of the pipes , used alone , takes 15hrs longer than the other to fill the tank .
1st pipe DATA;
Time = x hrs/job ; Rate = 1/x job/hr
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2nd pipe DATA:
Time = x+15 hrs/job ; Rate = 1/(x+15) job/hr
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how long would each pipe take to fill the tank alone?
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EQUATION:
rate + rate = together rate
1/x + 1/(x+15) = 1/10
Multiply thru by 10x(x+15) to get:
10(x+15) + 10x = x(x+15)
20x + 150 = x^2+15x
x^2-5x+150=0
(x-15)(x+10) = 0
Positive solution:
x = 15 hrs (time required for 1st pipe to do the job alone)
x+15 = 30 hrs (time required for the 2nd pipe to do the job alone)
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Cheers,
Stan H.
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