This study uses a mathematical model based on the temporally relaxed theory of Fick’s law to describe the one-dimensional (1D) non-Fickian transport of solutes in a layered heterogeneous porous medium. The methodology introduces two relaxation times to accurately consider solute particle collisions and attachment, resulting in the development of new advection-dispersion equations (ADEs) for each layer. In this scenario, it is assumed that each layer of the porous medium is initially contaminated by a background source. Additionally, we are taking into account a time-dependent input source located at the origin of the domain. The semi-analytical solution of the proposed model is obtained using Laplace Transform Techniques and a numerical inversion of the transformation. All graphic plots are obtained using MATLAB software. The results show that the temporally relaxed theory can reproduce the solutes transport behaviour described by the existing two-stage models, 1D equilibrium models in homogeneous and layered media. Additionally, relaxation times significantly affect the spatial distribution of solute concentration in layered media and the remediation time. This innovative approach provides a deeper insight into solute transport in layered media and its impact on groundwater contamination. It can serve as a preliminary tool for future researchers studying decaying solute migration such as radionuclides in groundwater and their impact on water quality.