Question 1207781
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15*20 = 300


Consider a 300 gallon bathtub. It turns out this volume doesn't really matter. There's nothing special about the 300. You can pick any other positive number and the final answer will be the same at the end.


The 300 gallon tub fills up completely in 15 minutes if both faucets are on and the drain is closed.
I'll assume that the tub starts off completely empty in this scenario.
The fill rate is 300/15 = 20 gallons per minute.
rate = amountDone/time


When both faucets are off and the drain is open, the 300 gallon tub empties in 20 minutes. 
I'll assume that the tub is completely full at the starting point of this scenario.
drain rate = 300/20 = 15 gallons per minute



Now let's consider the scenario where both faucets are on and the drain is open at the same time. It's an unfortunate waste of water. 
In this situation, the fill rate and drain rate basically play a game of tug-of-war. 
The fill rate wins out ultimately since the fill rate is larger compared to the drain rate (20 > 15).
The net fill rate is 20-15 = 5 gallons per minute.
Despite the drain wanting to remove the water, the faucets win out at the end of the day. Though of course it will take a bit longer to fill the tub. 


How long would it take for the tub to completely fill up in this case?
rate*time = amountDone
time = amountDone/rate
time = (300 gallons)/(5 gallons per min)
time = 60 minutes
time = 1 hour
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