Balance it out.

Consider the following steady-state open system, involving flow of three substances $\text{A,B}$ and $\text{C}$ :

Two streams $1$ and $2$ , of mass flow rates $\dot{m}_1$ and $\dot{m}_2$ respectively enter the first chamber. $\dot{m}_1$ has a variable mass flow rate of $\dot{m}_1(t)=(2t+3)\text{kg/s}$ where $t$ is time in seconds. Two other streams $3$ and $4$ , of mass flow rates $\dot{m}_3$ and $\dot{m}_4$ respectively exit it. These two streams which exit the first chamber also enter a second chamber, a reaction chamber. In this chamber, $\text{A,B}$ and $\text{C}$ react to form another substance $\text{D}$ through the reaction equation $4\text{A}+2\text{B}+\text{C}\rightarrow \text{D}$ . All excess reactants are ejected through another stream going out of the reaction chamber. Calculate the mass flow rate of $\text{D}$ after $2.5$ seconds, in $\text{kg/min}$ .

Additional information :

• Stream $1$ is $70\%$ $\text{A}$ and the rest $\text{C}$ .
• Stream $2$ is $60\%$ $\text{B}$ and the rest $\text{A}$ .
• Stream $3$ is $20\%$ $\text{C}$ and also outputs equivalent amounts of $\text{A}$ and $\text{B}$ .
• Stream $4$ comprises of only $\text{A}$ .
• Assume that $\text{A,B}$ and $\text{C}$ all have the same molar mass.