A simple scattering model is used to test alternative methods for calculating decay lifetimes, or equivalently, resonance widths. We consider the scattering of s-wave particles by a square well with a square barrier. Exact values for resonance energies and resonance widths are compared with values calculated from Wigner-Weisskopf perturbation theory and from the Garside-MacDonald projection operator formalism. The Garside-MacDonald formalism gives essentially exact results while the predictions of the Wigner-Weisskopf formalism are fairly poor.