  We present a realistic theoretical treatment of a three-level $\Lambda$
system in a hot atomic vapor interacting with a coupling and a probe field of
arbitrary strengths, leading to electromagnetically-induced transparency and
slow light under the two-photon resonance condition. We take into account all
the relevant decoherence processes including col5Blisions. Velocity-changing
collisions (VCCs) are modeled in the strong collision limit effectively, which
helps in achieving optical pumping by the coupling beam across the entire
Doppler profile. The steady-state expressions for the atomic density-matrix
elements are numerically evaluated to yield the experimentally measured
response characteristics. The predictions, taking into account a dynamic rate
of influx of atoms in the two lower levels of the $\Lambda$, are in excellent
agreement with the reported experimental results for $^4$He*. The role played
by the VCC parameter is seen to be distinct from that by the transit time or
Raman coherence decay rate.
