Fun with fuses

You are given two fuses, each of which burns for exactly one minute. However, since the fuses are not of uniform thickness, they do not burn at a uniform rate along their lengths. How can you use the two fuses to measure 45 seconds?

This puzzle was taken from Norman Do's regular Puzzle Corner column for the Gazette of the Australian Mathematical Society. Why not try your hand at the problems in the latest Puzzle Corner?

If you are stumped by last issue's puzzle, here is the solution.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.