You have to somehow break the time down into quarters, so... half then half again, so...
I'm typing this as I'm thinking it, so there's a high probability that by the end of this message, none of it will have made sense. But frankly I'm not awake enough this evening to get it clear in my mind.
You can get half an hour from one rope by lighting both ends of the rope. This way, even if the rope isn't uniform and the two fires don't meet in the exact middle, they'll still meet once half of an hour has passed.
Presumably you can then use the second rope... Yes, if you light one end of the second rope at the same time as you light both ends of the first, then after half an hour the first rope has burnt out and you'll still have 30 minutes of burning left on the second rope. But if you then light the other end of the second rope, it will burn in half the time again, 15 minutes. Which I believe is a total of 45 minutes.
Heck, with the muddle my brain is in right now, it'll probably be easier if I just go out, buy some rope and film the solution for youtube, rather than try to explain it coherently.