An iterative procedure is worked out for estimating solute travel times in a subsurface system by making use of the velocity and streamline distributions pertinent to the system. The developed method is then being applied to study the solute travel times to ditch drains originating from a field being subjected to a uniform (1) recharge and (2) ponding field over the surface of the soil. For case (1), both single and layered soils are being considered to estimate the travel times. The developed mathematical procedure is simple to use, robust, reasonably accurate even if being used with a lesser division of a streamline and completely eliminates the necessity of determination of any integrals for estimating the travel times-integrals which, in the methods generally been employed for estimating the travel times from steady-state analytical groundwater models, would otherwise need be evaluated. The study shows that travel times of water particles traversing through a layered soil being subjected to a uniform recharge at the surface are sensitive to the directional conductivities, anisotropy ratio (defined here as the ratio between horizontal and vertical hydraulic conductivities of soil) and thickness of individual layers of a soil profile as well as to the magnitude of the steady-state recharge on the surface of the soil. For the ponded drainage scenarios also, directional conductivities and thickness of a soil profile, extent of partial penetration and width of the ditch drains, levels of water head at the surface of the soil as well as on the ditches are observed to influence the travel times in a noticeable way. The proposed method is important as it provides simple and accurate estimations of migration times of pollutants to subsurface drains under different drainage situations; it can also be used to assess the time of reclamation of a salt-affected or waterlogged soil being drained by a network of subsurface drains being installed for the purpose from the available hydraulic theory relevant to the concerned drainage situation.