>>>Let each fuse burn for 15 minutes and extinguish them. The rest of each fuse will burn for 45 minutes.
>>>
>>>>You have two fuses of variable lengths.
>>>>
>>>>Each fuse burns for exactly 1 hour.
>>>>
>>>>Each fuse burns unevenly. ( example 1/10th of the fuse could burn for 50 minutes and the rest of the fuse could take 10 minutes. ) You don't know until after the fuse has burned up.
>>>>
>>>>Make the two fuses last exactly 45 minutes.
>>
>>You don't have a watch or any other way of telling time. How can you determine when 15 minutes is up?
>
>What else I don't have or cannot use? :)

Sorry about that, I forgot to add that.

The constraints of the puzzle are that you have matches and fuses and with those two things alone, you should be able to figure a way to burn the two fuses so they take 45 minutes.