Using a population number synthesis code, the theoretical time distributions of type Ia supernovae in starburst galaxies are calculated, using competing models for the formation of such events: the single degenerate (a white dwarf accreting matter from a late main sequence or red giant companion) and double degenerate (the merger of two white dwarfs) scenario. The code includes the latest results in determining the progenitors for both models. Examples are the mass stripping effect in the case of the single degenerate scenario and the differentiation between the α- (based on the balance of energy) and γ- (based on the balance of angular momentum) description of energy conversion during common envelope evolution of binaries. The shape and extent of the obtained delay time distributions critically depends on which formation scenario is used. Comparing these results to the latest observed distributions allows to draw conclusions about the constraints put on the theoretical models by these observations. We also specifically investigate the influence of the degree of conservatism during Roche lobe overflow on the delay time distribution. We conclude that the single degenerate scenario alone cannot reproduce the observed delay time distributions, and that most double degenerate type Ia supernovae are formed through a quasi-conservative Roche lobe overflow phase followed by spiral-in, as opposed to a double common envelope evolution.