A tank initially contains 300 gallons of salt-water solution in which 20 pounds of salt is dissolved. Salt-water solution with a concentration of 2 pounds of salt per gallon of solution is poured into the tank at a rate of 2 gal/sec. A drain is opened at the bottom of the tank allowing the salt-water solution to leave the tank at a rate of 5 gal/sec. (a) Write down the differential equation that describes the change in the volume of solution over time and solve it. (b) Write down the differential equation that describes the change in the content of salt over time and solve it. (c)How long does it take for the tank to drain completely? (d) How much salt will be dissolved in the tank at the time equal to half the time in part (c)?
A tank initially contains 300 gallons of salt-water solution in which 20 pounds of salt is dissolved. Salt-water solution with a concentration of 2 pounds of salt per gallon of solution is poured into the tank at a rate of 2 gal/sec. A drain is opened at the bottom of the tank allowing the salt-water solution to leave the tank at a rate of 5 gal/sec.
(a) Write down the differential equation that describes the change in the volume of solution over time and solve it.
(b) Write down the differential equation that describes the change in the content of salt over time and solve it.
(c)How long does it take for the tank to drain completely?
(d) How much salt will be dissolved in the tank at the time equal to half the time in part (c)?
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