The Dushman reaction taking place after the abrupt change of the absorbance in the Landolt reaction was followed by monitoring the concentration of triiodide spectrophotometrically in buffered solutions. The joint evaluation of the experimental data on the kinetic system (Landolt) and subsystem (Dushman) has revealed that the inverse of the Landolt induction time (t(i)) is proportional to the combination of the concentration and the square of the concentration of both the iodide and hydrogen ions, while the inverse of t(i) is linearly proportional to the iodate concentration. The hydrogen sulfite dependence, however, is found to be more complex; the Landolt induction time goes through a minimum as a function of hydrogensulfite concentration; the phenomenon that has not been reported yet. A kinetic model is suggested in which the rate law of both the Landolt and Dushman reactions is supplemented to take all the characteristics of the measured curves into account. It is demonstrated that the supercatalytic term of the Landolt reaction with respect to hydrogen ion discovered recently and the rate term of the Dushman reaction being first order with respect to iodide ion play an important role in explaining the dependencies of the Landolt induction period.