Burning rope

There are two lengths of rope.
Each one can burn in exactly one hour.
They are not necessarily of the same length or width as each other.
Moreover, they are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

By burning the ropes, how do you measure exactly 45 minutes worth of time?

Put the two ropes end-to-end so that they are touching. Light the non-touching end of one rope and watch it. When the fire reaches the other (touching) end immediately light the non-touching end of the second rope.

Because the ropes are touching, the touching end of the second rope should have been lit when the fire from the first rope reached it. This means that the second rope is now burning from both ends, when the fire from the two ends meet it will be 45 minutes from the time that you lit the first rope.

Originally posted by Mathurine
[b]There are two lengths of rope.
Each one can burn in exactly one hour.
They are not necessarily of the same length or width as each other.
Moreover, they are not of uniform width (may be wider in middle than on the end), thus burning half of the rope is not necessarily 1/2 hour.

By burning the ropes, how do you measure exactly 45 minutes worth of time?[/b]

Light both ends of one rope.. it will burn completely in 30 minutes. At the same time, light the second rope at one end. When the first rope is completely burned (30 minutes) the second rope has 30 minutes more left to burn. At that point, light the second end of the second rope.. the remaining piece will burn in 15 minutes. Elapsed time is 45 (30+15) minutes.

Originally posted by Fat Lady
Put the two ropes end-to-end so that they are touching. Light the non-touching end of one rope and watch it. When the fire reaches the other (touching) end immediately light the non-touching end of the second rope.

Because the ropes are touching, the touching end of the second rope should have been lit when the fire from the first rope reached it. This m ...[text shortened]... the fire from the two ends meet it will be 45 minutes from the time that you lit the first rope.

That would be 1:30. Each rope burns for 1 hour.

Originally posted by XanthosNZ
That would be 1:30. Each rope burns for 1 hour.

Exactly! HandyAndy got it right, though!

Originally posted by Mathurine
Exactly! HandyAndy got it right, though!

Nice problem! I know of a related question involving a monk climbing a mountain, but I'll save it for another thread.