Mixing Problems and Separable Differential Equations - Calculus 2

In this video, I will go over many examples about typical mixing problem that students often see in Calculus 2 classes. There is also another kind of mixing problem that involves percentages. I will cover this type of mixing problem in the next video. There are three formulas that you need to know. They will result in a separable differential equation that you can easily solve. A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of salt per liter of water enters the tank at a rate of 25 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt will there be in the tank after half an hour? A vat with 500 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 5 gal/min. The mixture is pumped out at the same rate. The solution is kept thoroughly mixed. What is the percentage of alcohol after an hour? A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10L/min The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. How much salt is in the tank: (a) after t minutes (b) after 1 hour? A tank contains 1000L of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank a) after t min? b) after 20 min?