Rate equations are exactly solved for the reversible consecutive reaction of the first-order and the time-dependence of concentrations is analytically determined for species in the reaction. With the assumption of pseudo first-order reaction, the calculation applies and determines the concentration of product accurately and explicitly as a function of time in the unimolecular decomposition of Lindemann and in the enzyme catalysis of Michaelis-Menten whose rate laws have been approximated in terms of reactant concentrations by the steady-state approximation.