SOLUTION: Hello, the question below has me stumped. It is from a homework handout so I do not have a textbook ISBN--sorry. Thanks in advance for your help. Two pipes can be used to fi

Question 190167: Hello, the question below has me stumped. It is from a homework handout so I do not have a textbook ISBN--sorry. Thanks in advance for your help.
Two pipes can be used to fill a tank. The smaller diameter pipe takes 4 hours longer to fill the tank than the larger diameter pipe. If both pipes are used together, it takes 10 hours to fill the tank. How long would it take each pipe working alone to fill the tank? Round to the nearest tenth of an hour.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two pipes can be used to fill a tank.
The smaller diameter pipe takes 4 hours longer to fill the tank than the larger diameter pipe. If both pipes are used together, it takes 10 hours to fill the tank. How long would it take each pipe working alone to fill the tank? Round to the nearest tenth of an hour.
-----------------------------------
Smaller pipe DATA:
time = x+4 hrs/job ; rate = 1/(x+4) job/hr
-----------------------
Larger pipe DATA:
time = x hrs/job ; rate = 1/4x job/hr
-----------------------
Together DATA:
time = 10 hrs/job ; rate = 1/10 job/hr
-------------------------
Equation:
rate + rate = together rate
1/(x+4) + 1/x = 1/10
Multiply thru by 10x*(x+4) to get:
10x + 10(x+4) = x(x+4)
20x + 40 = x^2 + 4x
x^2 - 16x - 40 = 0
x = [16 +- sqrt(16^2-4*1*-40)]/2
Positive answer:
x = [16 + sqrt(416)]/2
x = 18.2 hrs. (time for the larger pipe to do the job)
x+4 = 22.2 hrs. (time for the smaller pipe to do the job.)
======================================
Cheers,
Stan H.
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