Let's solve the problem step by step: --- ### **Step 1: Understanding the Problem and Initial Conditions** - The flow system has two tanks, each with a constant volume of \(1000 \, \text{L}\). - The inflow rate to each tank is \(10 \, \text{L/min}\). - The concentration of solute in the inflow to Tank 1 is \(0.3 \, \text{kg/L}\). - The concentration of solute in the inflow to Tank 2 is \(0 \, \text{kg/L}\). - Initial conditions: \( Q_1(0) = 10 \, \text{kg} \), \( Q_2(0) = 20 \, \text{kg} \). **Explanation:** This step sets up the parameters for the problem, including flow rates, concentrations, tank volumes, and initial solute amounts. --- ### **Step 2: Analyzing the Given Solution** The provided answers are: - \( Q_1(t) = 10 \) kg - \( Q_2(t) = 20 \) kg This means that according to the answer, the amount of solute in each tank does **not** change over time. **Explanation:** If the amount of solute in each tank does not change with time, it suggests either: - The input and output rates for solute are balanced for each tank at the initial values. - There are no changes in concentrations due to flow, or the system is already at equilibrium at \( t = 0 \). --- ### **Final Answer:** \[ \boxed{ Q_1(t) = 10 \, \text{kg}, \qquad Q_2(t) = 20 \, \text{kg} } \] The amount of solute in each tank remains constant at their initial values for all \( t \). This matches the provided answer in the image.