A WWTP generates $22\mathrm{.}0$ MGD of effluent and discharges it into a nearby river. The effluent has a temperature of $20C.$ The river has a flow rate of $12\frac{m^3}{s}$ and temperature of $15C$ in the wintertime. The effluent mixes with the river $($let$\text{'}$s call this the mixing point$).$ After the effluent has mixed with the river, the dissolved oxygen deficit is $2\mathrm{.}2m\frac{g}{L},$ and the BOD is $5\mathrm{.}4m\frac{g}{L}.$ The deoxygenation rate constant at $20C$ is $0\mathrm{.}6da{y}^{-1},$ and the reoxygenation rate constant at $20C$ is $0\mathrm{.}8$ day ${?}^{-1}.$ The river cross$-$section is $6m^2.$

a$)[18$ pt$]$ What is the travel time that corresponds to the critical deficit? $($i$.$e$.,$ critical time$)$ You can assume $L_a$ is equal to the given BOD. Please note that we need the travel time not the critical time