An analytical solution is obtained for the three-dimensional advection-dispersion equation describing the temporally dependent flow domain through an isotropic semi-infinite homogeneous porous medium by using the Laplace transformation technique. Also, a numerical solution is obtained by using the explicit finite difference method. The usage of dimensionless variables allows this solution to be applicable in a wide variety of cases. Impacts of different parameters controlling pollutant dispersion are studied with the help of graphs and a table. We discuss how to use the fact that the provided solution predicts pollutant concentration along the river to help in the decision-making regarding its remediation with effective methods. This paper mathematically indicates that releasing clean water from a barrage reduces the pollutant concentration in a river.