The Faddeev equations with separable two-body scattering amplitudes are used to calculate the binding energy of the three-alpha system. We find a value of the binding energy in reasonable agreement with the experiment value. Using separable potentials of the Yamaguchi, Tabakin, and Barbour-Schult types to generate the S-wave scattering amplitudes, we find the three-body bound state is not extremely sensitive to the form of the two-body interaction. We also find the admixed D-state contributes little to the three-body binding energy. With a view to future studies, a set of separable potentials is presented to describe neutron-alpha scattering.