We think that this is an interesting puzzle, which requires some thought "Outside the box" as it were.
You have two ropes and you know that each rope will take exactly one hour to burn completely. The bad news is that the rate of burn along the ropes is inconsistent; parts of them will burn more quickly and other parts will burn more slowly, and both ropes are different.
But you do know that the total burn time for both ropes is sixty minutes, even if you can't assume that when half of the length is burnt, 30 minutes have elapsed.
The challenge is to measure exactly three quarters of an hour (45 minutes) using these two ropes and as many matches as you want.
Light one end of one of the ropes and both ends of the other rope.
When the second rope has burnt out exactly 30 minutes will have passed, and you light the unlit end of the other rope.
As the first rope had been burning for 30 minutes it would have to have 30 minutes of burning time left. And as it is now burning from both ends it will burn out 45 minutes after you started.