In this paper, we explore the use of exact inference in hybrid Bayesian networks to compute the exact marginal distribution of project completion time. Activities durations can have any distribution, and may not be all independent. We model dependence between activities using a Bayesian network, approximate non-Gaussian conditional distributions by mixtures of Gaussians, and reduce the resulting hybrid Bayesian network to a mixture of Gaussian Bayesian networks. Such hybrid Bayesian networks can be solved exactly using Hugin, a commercially-available software package. We illustrate our approach using a small PERT network with five activities.