Tie the ends of the first rope together to make it into an O. That rope will burn in half an hour (because it burns in 2 directions).

Tie the ends of the second rope together, but then fold it over to make an 8 shape. If you start burning at the intersection, it will burn in 15 minutes (because it burns in 4 directions – thus 4 times faster).

Light one right after the other, and you got your 45 minutes.