Burn the ropes!

You have two ropes and a lighter. Each of the ropes burns out in exactly 60 minutes, but not at a uniform rate - it is possible for example that half of a rope burns out in 40 minutes and the other half in just 20. How can you measure exactly 45 minutes using the ropes and the lighter?


First you light up both ends of the first rope and one of the ends of the second rope. Exactly 30 minutes later the first rope will burn out completely and then you have to light up the other end of the second rope. It will take 15 more minutes for the second rope also to burn out completely, for a total of 30+15=45 minutes.