Two-state gated trapping systems with a static trap are solved by a first-passage-time-distribution (FPTD) approach. The intrinsic microscopic rate for either state need not be zero, an important condition toward developing a theory for gated trapping problems of multiple or continuous states. A one-state trap with a slower intrinsic rate is shown to be physically equivalent to a partially open trap with a faster intrinsic rate. This result is applied to explicitly express the two-state gated FPTD in terms of their corresponding ungated FPTD. Consequently, the gated trapping rates of the systems are calculated and discussed. An approach to experimentally determine gating mechanisms is also proposed.