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Question 551226: Filling a tank. Two pipes are connected to the same tank. Working together, they can fill the tank in 4 hr. The larger pipe, working alone, can fill the tank in 6 hr less time than the smaller one. How long would the smaller one take, working alone, to fill the tank?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Filling a tank. Two pipes are connected to the same tank. Working together, they can fill the tank in 4 hr. The larger pipe, working alone, can fill the tank in 6 hr less time than the smaller one. How long would the smaller one take, working alone, to fill the tank?
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Let x = time (hours) it takes for smaller one alone
then
x-6 = time (hours) it takes for larger one alone
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4(1/x + 1/(x-6)) = 1
multiplying both sides by x(x-6):
4((x-6) + x) = x(x-6)
4(2x-6) = x^2-6x
8x-24 = x^2-6x
-24 = x^2-14x
0 = x^2-14x+24
0 = (x-2)(x-12)
x = {2,12}
throw out the 2 (extraneous) because it doesn't make sense leaving:
x = 12 hours
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