[bonanova]

A tank is 5 feet deep. A and B are fill pipes. Four feet from the bottom is drain pipe C. A foot below that is drain pipe D. A foot below that is drain pipe E. A foot below that is drain pipe F. If the drain pipes are closed, A can fill the tank in 8 minutes, and B can fill the tank in 12 minutes. C can drain the the tank at a rate of 1 tank per hour. D can support a flow that would drain a tankful of water in 30 minutes. E would need 10 minutes, and F 15 minutes.

The drains are all opened, and the fill pipes go into action.

When will the water reach F?

How much later will the water reach E, if it does?

How much later will the water reach D, if it does?

How much later will the water reach C, if it does?

How much later will the water fill the tank, if it does?

[Guest]

A .625 FPM B .4166 FPM

C .083 29.5=46 = -.039 FPM

D .166 6.76 Minutes = .044 FPM

E .5 2 minutes = .21 FPM

F .33 = .96 miuntes+ .71 FPM

Bottom = + 1.041

Reaches F at about .96 Minutes

Reaches E at about 2 miuntes

Reaches D at about 6.76 minutes

Reaches C at about 29.46 minutes

Never fills

Edited April 19, 2008 by TySim

[Guest]

F in 57,6 sec

E 1 min 24,7 sec later

D 4 min 48 sec later

C 24 min later

never fills

[Guest]

Heres an explination of how I got my answer. It works (i think) .

in 12 min 2.5 tanks will be filled by pipes a+b this is equivilent to 12min=12.5 feet of water in the tank.

Divide by 12 to give how high the water is after every minute. Let this be Z.

now divide 1 by Z which gives the time it takes for the water to rise by one foot.

The water is now being drained by F so you now have to take away how much it can empty in a minute from Z

Pipe f empties 5 foot every 15 min so in 1 minute 0.333... of a foot is drained.

Takeing this away from Z gives the new speed at which the water rises. Let this be Y

Now divide 1 by Y and add the answer to the previous answer. Repeat with each other pipe until you reach C

Reaches F .96 Minutes

Reaches E 2.3717 ish minutes 1.411764706 minutes later

Reaches D 7.17176 ish minutes 4.8 minutes later

Reaches C 31.17176 ish minutes 24 minutes later

Never fills.

Same answer as = W = just shown in parts of a minute.

Edited April 19, 2008 by Mad Twit

[Guest]

I have the same answers as the previous posters.

I think this problem should read that drain F opens at the 1 foot mark, drain E at the 2-foot mark, etc. Otherwise, we're assuming these drains are infinitely thin and powerful to do what they do, instead of draining a little bit when the water mark barely reaches it and fully draining when the water is completely over it.

[bonanova]

I have the same answers as the previous posters.

I think this problem should read that drain F opens at the 1 foot mark, drain E at the 2-foot mark, etc. Otherwise, we're assuming these drains are infinitely thin and powerful to do what they do, instead of draining a little bit when the water mark barely reaches it and fully draining when the water is completely over it.

You're right, of course.

But the puzzle is about the math, and as we engineers often say, ignore the end effects.

I was going to make a drawing; in the end, I opted for a suggestive wording.

[Guest]

A tank is 5 feet deep. A and B are fill pipes. Four feet from the bottom is drain pipe C. A foot below that is drain pipe D. A foot below that is drain pipe E. A foot below that is drain pipe F. If the drain pipes are closed, A can fill the tank in 8 minutes, and B can fill the tank in 12 minutes. C can drain the the tank at a rate of 1 tank per hour. D can support a flow that would drain a tankful of water in 30 minutes. E would need 10 minutes, and F 15 minutes.

F: after 57.6 sec

E: 2 min 22 sec

D: 7 min 10 sec

C: 31 min 10 sec

The tank will never be filled.