A large tank is filled with 500 gallons of pure water. Brine containing 2lb of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at 10 gallons per minute. when is the tank empty?

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A large tank is filled with 500 gallons of pure water. Brine containing 2lb of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at 10 gallons per minute. when is the tank empty?

Mathematics
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If you take a basis of 1 minute, the change in volume is -10gal (out) + 5gal (in) = -5gal(net). So the rate of change in volume of the tank is -5 gallons per minute. It therefore takes 100 minutes to empty the tank\[\frac{500{gal}}{5gal/\min}=100\min\]

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