Question

1. Anthony works at a plant that makes a solution for brining hotdogs. A tank with a capacity of 2000 liters originally contains 1500 liters of fresh distilled water. Two pipes pour different mixtures of brine into the tank. The big pipe pours 1 kg of salt per minute at a rate of 6 liters per minute. The smaller pipe pours a mixture containing 2 kg of salt per minute at a rate of 4 liters per minute. Assume the salt and water are well mixed.

1. If the mixture flows out of two pipes at a rate of 5 liters per minute each, what is the amount of salt in the tank at any time . What is the amount of salt at 10 minutes? Does solution reach a steady state of salt and if so, what is it? Graph the solution.

2. Anthony accidentally shuts off one of the outflow pipes and doesn’t notice. When will the tank overflow and how much salt will it contain? Graph the solution.

3. He notices that the tank is overflowing and turns off the big pipe. How long will it take for the tank to return back to 1500 liters of the mixture. What will happen in the long run? Graph the solution.

Answer 1