Puzzle #140: Confusing?

You have some fuses that take one hour to burn from end to end.  They are made out of handwavium.  This substance lets me stick in a statement that while a fuse will burn out in exactly one hour, the fuse does not necessarily burn at an even rate.

You have no way of telling time or timing intervals by conventional means (watch, cell phone, sun, stars, etc.).  Using one or more fuses, how can you measure a one hour and fifteen minute interval?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 10, 2016 at noon Pacific Time. I will post the answer shortly after.