We use recent observations of type Ia Supernova (SN Ia) rates to derive, on robust empirical grounds, the distribution of the delay time (DTD) between the formation of the progenitor star and its explosion as a SN. Our analysis finds: i) delay times as long as 3-4 Gyr, derived from observations of SNe Ia at high redshift, cannot reproduce the dependence of the SN Ia rate on the colors and on the radio-luminosity of the parent galaxies, as observed in the local Universe; ii) the comparison between observed SN rates and a grid of theoretical single-population DTDs shows that only a few of them are possibly consistent with observations. The most successful models are all predicting a peak of SN explosions soon after star formation and an extended tail in the DTD, and can reproduce the data but only at a modest statistical confidence level; iii) present data are best matched by a bimodal DTD, in which about 50% of type Ia SNe (dubbed prompt SN Ia) explode soon after their stellar birth, in a time of the order of 10^8 years, while the remaining 50% (tardy SN Ia) have a much wider distribution, well described by an exponential function with a decay time of about 3 Gyr. This fact, coupled with the well established bimodal distribution of the decay rate, suggests the existence of two classes of progenitors. We discuss the cosmological implications of this result and make simple predictions. [Abridged]
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