The abundances of long-lived radioactive elements Th and U observed in metal-poor halo stars can be used as chronometers to determine the age of individual stars, and hence set a lower limit on the age of the Galaxy and hence of the universe. This radioactive dating requires the zero-decay productions of Th and U, which involves complicated r-process nucleosynthesis calculations. Several parametric r-process models have been used to calculate the initial abundance ratios of Th/Eu and U/Th, but, due to the sharp sensitivity of these models to nuclear physics inputs, the calculations have relatively large uncertainties which lead to large uncertainties in the age determinations. In order to reduce these uncertainties, we present a simple method to estimate the initial productions of Th and U, which only depends on the solar system abundances and the stellar abundances of stable r-process elements. From our calculations of the initial abundance ratios of Th/Eu and U/Th, we re-estimate the ages of those very metal-poor halo stars with published abundances of Th and U. Our age estimates are consistent, Within the errors, with the other age determinations derived from r-process models, and offer useful constrains for r-process theoretical calculations. The advantages and limitations of our simple method of radioactive dating are discussed.