You have 2 identical ropes which burn at a specific rate, and an unlimited supply of matches. When you light one end of a rope, the fire will take exactly 1 hour to travel to the other end of the rope.
You need to measure exactly 45 minutes. You must start by lighting one or both of the ropes. You can light or extinguish either end of either rope later, but you must only do this immediately after a rope has finished burning, as this is the only accurate way to measure elapsed time. You also must not light anywhere but the end of a rope, or any other form of guessing. You may finish with or without any remaining rope.