Linear and nonlinear versions of time dependent density functional theory are solved for a single solute particle in a simple binary solvent. All particles interact with Lennard-Jones potentials. The theoretical results are compared with molecular dynamics calculations. It is shown that the nonlinear theory is necessary in order to obtain a good quantitative description of selective solvation dynamics. The linear theory is only of qualitative value. Also, attention is drawn to a previously little appreciated problem which arises when one attempts to compare time dependent density functional theory with computer simulation or experimental results. The difficulty involves matching the theoretical and absolute time scales and is discussed in detail in this paper.