A simplified model, to that produced previously by the authors, for the galvanostatic discharge of primary alkaline battery cathodes is presented. Laplace transform and perturbation methods are employed to obtain the leading order spatial and temporal behaviour of the porous cathode over two distinct size scales. It is shown that for a wide range of industrially relevant discharge conditions the time taken for KOH electrolyte to diffuse into a porous electrolytic manganese dioxide particle is fast compared with the cathodic discharge time and that ohmic losses within the graphite phase of the cathode can be considered to be negligible. Numerical solution of the simplified model equations is discussed and the results are validated against relevant experimental data.