SOLUTION: There is tank that holds 400 gallons of water. You've got one pipe that can fill it up in 15 minutes. Another pipe can empty it in 40 minutes. If both pipes are open at the same ti
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-> SOLUTION: There is tank that holds 400 gallons of water. You've got one pipe that can fill it up in 15 minutes. Another pipe can empty it in 40 minutes. If both pipes are open at the same ti
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Question 322437: There is tank that holds 400 gallons of water. You've got one pipe that can fill it up in 15 minutes. Another pipe can empty it in 40 minutes. If both pipes are open at the same time, how long does it take to fill the tank? Found 2 solutions by ptaylor, Edwin McCravy:Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let t = time it takes to fill the tank when both pipes are open
One pipe fills at the rate of 1/15 tank (or 400/15 = 26 2/3 gal) per min
The other pipe empties at the rate of 1/40 tank (or 400/40=10 gal) per min
Together they fill at the rate of 1/15 - 1/40= 8/120 - 3/120=5/120 tank (or (5/120)*400=16 2/3 gal per min
So our equation to solve is:
(16 2/3)*t=400 or
(50/3)t=400
50t=1200
t=24 min
CK
In 24 min one pipe fills 26 2/3 * 24 or (80/3)*24=640 gal
In 24 min other tank empties 10*24 or 240 gal
640-240=400
400=400
Hope this helps---ptaylor
You can put this solution on YOUR website! There is tank that holds 400 gallons of water. You've got one pipe that can fill it up in 15 minutes. Another pipe can empty it in 40 minutes. If both pipes are open at the same time, how long does it take to fill the tank?
Make this chart:
No. of
tanks Time in Rate in
filled minutes tanks/minute
fill pipe
drain pipe
both together
Let x = the number of minutes to fill the tank when both are open.
Fill x in for the time for "both together". Also fill in the given
times for the two pipes indivisuallty, 15 and 40 minutes:
No. of
tanks Time in Rate in
filled minutes tanks/minute
fill pipe 15
drain pipe 40
both together x
Next fill in the number of tanks filled. The drain pipe "fills"
"negative one" tanks. (To drain one tank is considered the same
mathematically as "filling negative one tanks"). So we fill in
for the number of tabks "filled":
No. of
tanks Time in Rate in
filled minutes tanks/minute
fill pipe +1 15
drain pipe -1 40
both together +1 x
Next we fill in the rates by dividing tanks by minutes:
No. of
tanks Time in Rate in
filled minutes tanks/minute
fill pipe +1 15 +1/15
drain pipe -1 40 -1/40
both together +1 x +1/x
Make the equation from
Rate of fill pipe + Rate of drain pipe = Reate of both together
Multiply through by LCM of 120x:
Answer: 24 minutes
Edwin
