Question: Your target is to measure 45 minutes after being given two ropes and a lighter. Each rope will burn at precisely 1 hour. But the rate at which they burn is not constant so you can’t simply measure half of the length and burn to that point. Also each rope has different rate of burning along its length.
Answer : Light both the ends of one rope, and light one end of the other. Once the rope that was lit on both end completely burns you would know 1/2 an hour has gone by and the rope still burring has 1/2 hour of life left. Light the other end of that rope and now its ½ hour of life will be split to 15 minutes. Once it is burned you would know that 45 minutes (30+15) have gone by.