Revisit HW$4$ Question $4$ with two tanks in which pure water was flowing from the outside into tank I which gave you a homogeneous systems of ODES to solve. For this question of HW$5,$ instead of pure water, assume an inflow of $4ga\frac{l}{m}in$ of solution containing $1l\frac{b}{g}al$ of salt from the outside into tank $T_1.$ In addition, the $2ga\frac{l}{m}in$ flow to the outside from Tank $1$ was turned off with the flow from Tank $2$ to Tank $1$ remaining the same at $2ga\frac{l}{m}in.$ This necessitated increasing the flow rate from Tank $1$ to Tank $2$ to $6ga\frac{l}{m}in,$ and the flowrate from Tank $2$ to the outside to $4ga\frac{l}{m}in$ to maintain the constant or steady volume within the tanks and overall system. If tank sizes and initial salt contents remain the same, draw the new flowchart, rederive and solve the fundamental nonhomogeneous systems of design relationships $($ODEs$)$ to find the amount of salt $y_1(t)$ in $T_1$ and $y_2(t)$ in $T_2$ with time $t.$ How long would it take the system to circulate for the salt content $y_1(t)$ to equal $y_2(t)?$ What happens over a long period of time $($i$.$e$.,$ as $t).$ You may assume the contents of the tanks are kept uniform by mixing. Calculate all values, including eigenvalues, to $3$ significant figures.