SOLUTION: Can you please help me to set up this word problem and solve? Thank you. At Four Mile Island, there are two pipes that carry water to the nuclear reactor chamber. The first pi

Question 286901: Can you please help me to set up this word problem and solve? Thank you.
At Four Mile Island, there are two pipes that carry water to the nuclear reactor chamber. The first pipe can fill the reactor chamber in 4 minutes; the second pipe can fill the reactor chamber in 6 minutes. The drain can empty the reactor chamber in 12 minutes. How long will it take both pipes to fill the chamber if the drain is left open?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes both pipes to fill the chamber if the drain is left open
With the drain open, both pipes fill at the rate of 1/x chamber per min
First pipe fills at the rate of 1/4 chamber per min
2nd pipe fills at the rate of 1/6 chamber per min
But the drain empties at the rate of 1/12 chamber per min
So, with the drain open, both pipes fill at the rate of
1/4 + 1/6 - 1/12 chamber per min. Our equation to solve then is:
1/4 + 1/6 - 1/12=1/x multiply each term by 12x
3x+2x-x=12
4x=12
x=3 min----amount of time it takes both pipes to fill the chamber if the drain is left open
CK
in 3 min first pipe fills (1/4)*3=3/4 chamber
in 3 min 2nd pipe fills (1/6)*3=1/2 chamber
in 3 min drain empties (1/12)*3=1/4 chamber
3/4 + 1/2 - 1/4 should equal 1 (1 chamber, that is)
3/4 + 2/4 -1/4=4/4=1
1=1
Hope this helps---ptaylor
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