In this paper we address a problem of transient mass transport within a homogeneous domain to a drainage slit on an impervious basis. The statement and solution of the flow problem are well-known and are used as a starting point in our investigation. Using the comparison method introduced in general form by one of us, a simple, closed form estimation of the two-dimensional concentration field and of the solute flux is obtained. Conditions for the applicability of the method are derived and the influence of parameters on the solution are discussed.