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Question 158339: A tank has a supply pipe and an exhaust pipe. The exhaust pipe takes 5 minutes longer to empty the tank than for the supply pipe to fill it. If both are open, it takes the supply pipe 30 minutes to fill the tank. Find how long it takes the supply pipe to fill the tank when the exhaust tank is closed?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=amount of time it takes the supply pipe to fill the tank when the exhaust pipe is closed
So, the supply pipe fills at the rate of 1/x tank per min
And x+5=amount of time it takes the exhaust pipe to empty the tank
So, the exhaust pipe empties at the rate of 1/(x+5) tank per min
If both are opened, the tank fills at the rate of (1/x)-1/(x+5) tank per min and we are basically told that this equals 1/30 tank per min, so our equation to solve is:
(1/x)-1/(x+5)=1/30 multiply each term by x(x+5)*30
30(x+5)-30x=x(x+5) get rid of parens
30x+150-30x=x^2+5x subtract 150 from each side and simplify
x^2+5x-150=0 quadratic in standard form and it can be factored
(x+15)(x-10)=0
x=-15 min------------------------no good!! times in this problem are positive
and
x=10 min----------------------amount of time it takes the supply pipe to fill the tank when the exhaust pipe is closed
CK
(1/10)-(1/15)=1/30
(3/30)-(2/30)=1/30
1/30=1/30
Also
Hope this helps---ptaylor
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