You have two matches, and two fuses (pieces of string) which each burn for 30 seconds, and a bomb which must go off exactly 45 seconds after you light the fuse.
How do you determine exactly 45 seconds, using just these two matches and two fuses?
Note: Cutting one fuse in half won’t solve the problem because the fuses are of different thicknesses, and you can’t be sure how long any cut piece will burn.
Augmental 
Attach one of the fuses to the bomb, and use the matches to light the other at both ends (simultaneously). When the two burning ends meet, touch the first fuse to that, throw and run.
Oldtimer
It’s a good idea, and I think it’s on the right track for determining 15 seconds, but I don’t think it achieves the stated goal: a bomb that goes off 45 seconds after you light the fuse (and presumably run). It seems to me you’ve hung around for 15 seconds too many, but I could be wrong.
I think I would have lit both ends of fuse #1 with one match, and saved match #2 for fuse #2, but unfortunately, I can’t think of a “light one match and run” idea! I could do it with 3 30-second fuses…
Fold one fuse in half.
Take the first fuse and light it for 15 seconds, then turn it off. You then have a 15 second fuse and a 30 second fuse adding up to exactly 45 seconds !