another fraction word problem

I tried to figure out this question..and started it, but do not know how to continue....would anyone we able to give me a hand ??

An airline passenger read for the first 1/9 of the flight, and watched the film for the next 8/15 of the flight. He managed to sleep for 3/4 of the remaining time. When he woke they were serving snacks, which filled another 20 minutes. After that there was only 1/45 of the total flight time left. How long did he sleep?

Would anyone be able to draw a simple diagram...to explain this?

I tired looking for the common denominator by adding all the fractions together..

1/9+8/15+3/4+1/45=17/12

then i dont know what to do ><