Temporal aspects of the dynamic behavior of biochemical pathways in stationary states have been described by a transition time tau, which is the ratio of the sum of the pool concentrations of chemical intermediates to the flux for a given stationary state. In this paper, a related random variable is introduced, the transit rime theta, which is defined as the age of (metabolic) intermediates at the time of leaving the system. The theory, based on a semi-stochastic approach, leads to calculations of the probability distributions of the ages of the intermediates, as functions of time. By assuming that the kinetics of the pathway is described by mass-action laws, a system of partial differential equations is derived for the distribution function of the transit time. By using the method of characteristics the solving of the evolution equations for the distribution function is reduced to the solving of the kinetic equations of the process. The method is applied to a simple enzyme-substrate reaction operated in two different regimes : (1) with a constant input of reagent and (2) with a periodically varying input. In the first case the transit time probability distributions in the steady state are calculated both analytically and numerically. The mean transit time, calculated as the first moment of the distribution, coincides with the transition time calculated in the literature. In addition, the presented approach provides information concerning the fluctuations of the transit time. For a periodic input, the distribution function of transit times can be evaluated semianalytically by using the technique of Green functions. We show that in this case the distribution oscillates in time, and both the distribution of the transit time and its different moments and cumulants oscillate.