The fuses burn at uneven rates, but you know that when 30 minutes of fuse burn there is still 30 minutes of fuse left no matter what its length.   Knowing this light one fuse at both ends, and light the other fuse at only one end.  When the fuse lit at both ends is done 30 minutes have elapsed.  This means there is 30 minutes left on the fuse you lit at one end.  Quickly, light that fuse at the other end.  When this piece finishes then 15 minutes more will elapse.  Total time is 30 minutes plus 15 minutes.