A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drains from the tank at the rate 7 L/min. Let y o u be the number of kg of salt in the tank after t minutes. The differential equation for this situation would be:
Accepted Solution
A:
Answer:dy/dt = 7y / (t − 1000)Step-by-step explanation:Change in mass of salt = mass of salt going in − mass of salt going outdy/dt = 0 − (C kg/L × 7 L/min)where C is the concentration of salt in the tank.The concentration is mass divided by volume:C = y / VThe volume in the tank as a function of time is:V = 1000 + 6t − 7tV = 1000 − tTherefore:C = y / (1000 − t)Substituting:dy/dt = -7y / (1000 − t)dy/dt = 7y / (t − 1000)If we wanted, we could separate the variables and integrate. But the problem only asks that we find the differential equation, so here's the answer.