Angular distributions of the {sup 54}Fe({ital p},{ital n}){sup 54}Co and {sup 54}Fe({ital n},{ital p}){sup 54}Mn cross sections have been measured to test the Gamow-Teller sum rule ({ital S}{sub {minus}}{minus}S{sub +}=3(N{minus}Z)) in a case where the Gamow-Teller strength is large for both channels. The results for {ital S}{sub {minus}} and {ital S}{sub +} are compared to several models which have moderate success in describing the data. Large scale shell-model and quasiparticle random-phase-approximation calculations correctly predict the distribution of Gamow-Teller strength but overestimate the total strength. A model that approximates the nuclear surface to be a semi-infinite slab describes the cross sections well in the quasielastic scattering region if 2p-2h correlations are included.