How many times longer does a 0.50 -M star fuse hydrogen at it's core than does a 1.5 -M star?

Answer 1

The absolute magnitude of the 0.5 mag star is 1.0 Mag higher than the +1.5 magnitude star. Each magnitude corresponds to a factor of 10^0.4 = 2.512 higher power output, and the same factor higher hydrogen fusion rate, assuming the star is not burning helium as well. In other words, you have to assume that it is a Main Sequence star.