Analytical Question #7

There are two fuses which burn at different rates among themselves and between themselves. They only burn for one hour. For example, one could burn the entire way except one inch in a minute, then spend the last 59 minutes on that last inch. How can you exactly time 45 minutes using them?

• Light both ends of Fuse 1 and one end of Fuse 2 at the same time.
• Fuse 1 will exactly take 30 minutes to burn out since it started burning on both the ends at the same time.
• Light the other end of Fuse 2 the instant after Fuse 1 burns out.
• At that point Fuse 2 has burned for 30 minutes and has 30 minutes remaining. From this point Fuse 2 will exactly take 15 minutes to burn out as the remaining burning time will be halved.

So the total time is 30 + 15 = 45 minutes.