How to measure 45 minute by burning a fuse?

Question

You are provided two fuses. Each will burn for exactly one hour. But the fuses are not necessarily identical and do not burn at a constant rate. There are fast-burning sections and slow-burning sections. How do you measure forty-five minutes using only the fuses and a lighter?

Answer 1

At time zero, light both ends of fuse A and one end of fuse B. The fuses must not touch each other. It takes thirty minutes for fuse A's two flames to meet. When they do, there is exactly thirty minutes left on fuse B. Instantly light the other end of (still-burning) fuse B. The two flames will now meet in fifteen minutes, for an elapsed time of forty-five minutes.