An assessment is made of the accuracy of the variational method for calculating neutron reaction rates in plane foils in problems involving velocity-dependent cross sections. This is achieved by using a separable scattering kernel and cross sections which are inversely proportional to velocity, thereby allowing the problem to be solved by analytic methods. We find that the error in the reaction rate, as calculated by the variational method, is at most 7%. This error is an order of magnitude larger than that incurred in one-speed calculations.