A friend recently presented this puzzle and I am completely lost about the solution. There is probably an obvious solution, but I can't figure it out. Well, here it goes...

There are two threads. Each of them will burn for exactly one hour if one of its sides is set on fire. How can one measure 45 minutes exactly, using only these threads and a lighter (no regularity can be assumed on the physical structure of the threads, and they are not promised to be identical)?

Give this

Light 1 end of 1st thread and both ends of the 2nd thread. When the second thread is burnt up there is half an hour left to burn on the 1st thread. At this point light the other end of the first thread causing the final section to burn twice as quickly or in 15 minutes.

Total time 45 minutes.

Light one end and wait for 3 segments to burn.