We present a detailed theoretical treatment of a three-level Λ 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 collisions. 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 Λ, are in excellent agreement with the reported experimental results for H4 e. The role played by the VCC parameter is seen to be distinct from that by the transit time or Raman coherence decay rate. © 2009 The American Physical Society.