We consider a variant of probabilistic timed automata called parametric determinate probabilistic timed automata. Such automata are fully probabilistic: there is a single distribution of outgoing transitions from each of the automaton's nodes, and it is possible to remain at a node only for a given amount of time. The residence time within a node may be given in terms of a parameter, and hence we do not assume that its concrete value is known. We claim that, often in practice, the maximal expected time to reach a given absorbing node of a probabilistic timed automaton can be captured using a parametric determinate probabilistic timed automaton. We give a method for computing the expected time for a parametric determinate probabilistic timed automaton to reach an absorbing node. The method consists in constructing a variant of a Markov chain with costs (where the costs correspond to durations), and is parametric in the sense that the expected absorption time is computed as a function of the model's parameters. The complexity of the analysis is independent from the maximal constant bounding the values of the clocks, and is polynomial in the number of edges of the original parametric determinate probabilistic timed automaton.