Question about the physics.?

Question

Container A holds 100 gallons of water.
Hose B releases 10 gallons of water per hour into A.
Drain C leaks 10 gallons of water per hour when A holds 100 gallons of water and C leaks 0 gallons of water per hour when A is empty.

If A starts with 0 gallons of water when Hose B is turned on and Drain C is made, how long in hours will it take for Container A to hold at least 99 gallons of water?

If this problem is to hard to answer please answer with why.

Thank you.

Amy · Accepted Answer

Not given is how much C leaks when A is anywhere between empty and full.

If the drain is at the bottom of container A, then the speed at which it leaks could be proportional to the pressure and therefore the height of the water.
Assuming this, then C = A/10, then the volume in A at time t is given by:
A = 100 - 100 e^(- t/10)
Filling A to 99 gallons takes approximately 46 hours. (exactly, 20 ln(10))

On the other hand, if C is a safety drain at the top of container A, then it doesn't do anything until A is full.
A = 10t
Filling A to 99 gallons takes 9.9 hours.

bigbangs050695 · Answer

Are you looking for a whole number? Ok, so A is empty. Hose B pours in 10 gallons per hour. A does not start to drain through C until it is full, but it reaches it's required limit BEFORE it begins to empty, so we can ignore C. B empties 10 gallons per hour. We need 99 gallons. So 10 hours would take us to 100 gallons, But we need a gallon less, which is a tenth of what is poured in per hour. So 1/10 gallons takes a tenth of 60 minutes, which is 60/10 = 6. 60 - 6 = 54 ( as we're working backwards from 100), so it takes 9 hours and 54 minutes, (or 10 if you're working in whole hours) for the container to fill.

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