Assuming you only need to measure 45 minutes and can be present the whole time (rather than needing to light and leave) then the following should work...
light both ends of one fuse, and at the same time light one end of the second fuse. The fuse with both ends lit will be completely burnt in 30 minutes, at this point light the other end of the second fuse which will then take a further 15 minutes to burn out completely.