How about this:

fold the first cord at the middle (you can make sure this is the case by making sure the opposite ends meet when folded), and light it up (such that both ends start burning at the same time)

While it is burning (and it should take 30 minutes) fold the other cord twice (so that you have it in quarters).. once the first cord finishes burning, light the other cord (such that all four bits start burning).. this should take 15 minutes, and you have a total of 45!

ok, so technically, you might argue that the parts might burn eachother, but you can always space them out such that they don't!

I don't think this would work. All four bits would have to be burning the whole time for it to work. However, one of the four might burn almost instantly leaving a different piece to burn for a pretty long time. The value in burning both ends of the rope is that you know the rope is being consumed twice as fast for the entire period. If one of the four bits burns faster than the others, then the rope is only being consumed at the pace of three flames instead of four. Since we're not sure how fast each bit will burn, we can't do it this way.