Mathematical studies of solute transport in porous media have often utilized “equivalent” models of the transport process to remove undesired variability in the transport coefficients at the space and time scales of direct interest. Both deterministic and stochastic approaches in this genre produce an “effective” convection- dispersion equation with time-dependent coefficients. This type of equation in one spatial dimension is investigated mathematically in the present paper. A closed-form solution of the solute transport equation is derived for a semi- infinite spatial domain with arbitrary initial and boundary flux conditions. It is shown that the solution reduces to well-known results for special forms of the time-dependent coefficients. In general, however, a Volterra integral equation of the second kind must be solved to evaluate the analytical solution of the transport equation. We present a stable and convergent numerical scheme, utilizing a trapezoidal quadrature rule, for the solution of the Volterra equation. The method of solution developed should be applicable to a broad variety of solute transport problems, including particularly those in heterogeneous porous media.