Calculating Main Sequence Lifetime.

[adwodon]

1. Calculate the main sequence lifetime in years of a 10-M_\odot star if it has luminosity of 10⁴L_\odot and 10% of its mass will be converted from hydrogen to helium in the core. What will the end state of this star be?

Ok so I wasn't really sure what to put for working here as I have no idea where to begin, I've been searching around for a formula or something to calculate the lifetime but my lecturers notes are very vague and not helpful at all and numerous different google searches haven't helped in giving me a straight answer.

I found this formula somewhere but it doesn't make sense to me:

t_ms\approx\frac{M}{L}

Its part of a larger question involving the Hertzsprung Russell diagram which I've done however this bit I am totally stumped, if any of you guys could point me in the right direction or explain it to me i'd really appreciate it.

Oh and I should point out this is from a past paper, the only relevant information I could imagine is given to help on the front of the paper is (excluding the standards like Planck / speed of light etc):

Solar mass: 2x10³⁰kg
Solar Bolometric Luminosity: 3.9x10²⁶W

 

[adwodon]

Ok so I used E=mc^2 and got the total energy of the converted material as 6x10^38J
Which would sustain that luminosity for 5 years...

Thats roughly the same answer I got from the equation in my original post but I thought it was wrong because 5 years seems waaaaay too short.

Is that a plausible answer?