$3\mathrm{.}10.$ An isothermal, irreversible reaction

$A,-{?}^k,B$

takes place in the liquid phase in a constant$-$volume reactor. The mixing is not perfect. Observation of flow patterns indicates that a two$-$tank system with back mixing, as shown in the sketch below, should approximate the imperfect mixing.

Assuming $F$ and $F_R$ are constant, write the equations describing the system.