The Fuses

This is a two-part riddle.

Part 1: You have two irregular string fuses.  They burn unevenly, at unpredictable rates (slow, then fast, then maybe slow again - you don't know).  The one thing you DO know is that when either one is lit at one end, it will burn for exactly one hour.  So if you lit one, then the other in sequence, you would be able to measure out two hours.  As it turns out, however, you need to measure exactly 90 minutes.  The fuses can only be lit on the ends - not in the middle - and all you have is the fuses and a lighter.  How do you get an hour and a half?

Part 2: Using another pair of the same kind of 1-hour string fuses, how do you get 45 minutes?









Solution to Part 1: Light both ends of one fuse and it will burn for 30 minutes.  As soon as it burns out, light one end of the other fuse and it will burn for another 60 minutes.  30+60 = 90 minutes total.

Solution to Part 2: Light both ends of one fuse and one end of the other fuse at the same time.  When the fuse with both ends lit burns out, 30 minutes will have passed.  At that point, light the other end of the other fuse.  It will have been burning for 30 minutes and therefore will have 30 minutes left on it.  But when you light the other end of it, that time gets cut in half, so it will burn for 15 minutes more.  The original 30 plus 15 equals 45 minutes.