The Rope Fuse
A rope fuse is designed to take exactly one hour to burn its entire length. But the manufacturer has deliberately designed this fuse such that it does not burn evenly with time, thus, for example, it will not necessarily burn half its length in 1/2 hour.
You have no watch, but do have two such fuses and a match in your possession. You want to know when precisely 45 minutes has passed. What do you do?