A 100-liter tank initially contains 10 kg of salt dissolved in water. Starting at t=0 minutes, brine with a constant concentration of 0.50 kg L−1 enters the tank at 3 L min−1, and the well-mixed solution leaves at the same rate. Assume uniform mixing throughout.
(a) Formulate a differential equation for Q(t), the mass of salt (in kg) in the tank at time t.
(b) Solve the differential equation using the initial condition Q(0)=10.
(c) Determine the time, to the nearest minute, required for the mass of salt in the tank to reach 30 kg.