Starting with the Friedmann-Robertson-Walker (FRW) cosmological model, we can find an explicit solution for the scale factor a(t) using the baryotropic equation of estat and the Friedmann equation. This barotropic equation describes several types of matter (energy): non-relativistic matter, radiation and vacuum energy (cosmological constant), therefore exists an explicit expression for a=a(t) that at the same time relates to a density of energy ρ=ρ(t) for each component. It is considered that each stage of the Universe was dominated by one type of material, and the expressions that describe the time evolution are independent each other. By using experimental data from [1] the calculations of the age of the Universe for each type of matter are carried out