A relatively simple mathematical derivation is employed to obtain the relationship between the solute concentrations and their velocities along the column. These equations are used to calculate numerically the breakthrough curves and delineate the elution behaviors of competing solutes in the chromatographic column. A hodograph constructed from the derived equations using published data for the coupled adsorption isotherms is adopted to visualize the concepts of the shock and the diffusive waves. The resulting elution curves at different column lengths show a successful application of the scaling relationship between the column length and feed period to the nonlinear coupled system.