Printable View
You are given 2 lengths of rope and a lighter. You are told that each rope when lit will burn up in one hour. The ropes do not burn at a constant rate and they are of different lengths. Your task is to measure 45 minutes of elapsed time using nothing but the ropes and the lighter. Good luck!
I'd time the 45 minutes on my watch and burn the ropes for fun at my leisure.
Hmmm. The ropes both will burn for 1 hr each at difference rates so the length is not the concern, the % of rope burned is the issue.
I would fold and cut them into 1/2 and then again to get quarters out of each rope then burn 3/4's of them to get the 45 min burn time.
Correct??
Will N.
Light one of the ropes at each end so it burns toward the middle. At the same time light only one end of the other rope. Since the first rope is burning twice as fast as it would if only one end was burned it will take 30 minutes. When the 30 minutes are up the half rope remaining will have 30 minutes of burn time left. Now light the other end of the second rope so it is now burning at both ends. This will give another 15 minutes of burning. Total time = 45 minutes.
This means they burn at a variable rate. The solutions above, if I understand them correctly, rely on each rope burning at a constant but different rate. I'm puzzled so far...Quote:
Originally Posted by thebigspendur
Even if they burn at a variable rate the entire ropes are consumed for my solution making the variability no longer a factor. Hey big spender - whatcha think?
Yeah, but when you account for the time spent lighting each end, you're up to 46 minutes. ";"Quote:
Originally Posted by Ogershok
This makes my head hurt...:thinking:
It's true the variability factor is taken care of in your solution, but you're assuming the rope will burn in 30 minutes when lit from both ends. However the problem states that you are told the rope will take an hour to burn "when lit." If you were told that the rope when lit "at one end" will burn in an hour, then your solution works. Or am I reading the problem too narrowly? Maybe it is supposed to be a given that if I light the entire rope at once, it will not take an hour to burn ie. maybe it is possible to trick the ropeQuote:
Originally Posted by Ogershok
I think thebigspendur has been smoking his rope, discovered he'd been drifting and can't find the fifteen minutes he lost. :)
We hang one of the ropes perfectly vertical, wait for the North Star to be out, so we can position the other rope pointing perfectly north, and then we have a makeshift sundial. The following day, assuming it's not overcast we can put some graduations around our sundial, and calculate 45 minutes.
The lighter is there to help us see what we're doing whilst tying the ropes up in the dark.
Good trick question Mr. Spendur. Give us a hard one next time!
A winner I think.Quote:
Originally Posted by Ogershok
Burning one of the one hour ropes does get you 30
min.
Now how to burn the second one hour rope in 15 min?
Since you have had it burning from only one end for 30
min already then doubling it back to burn from both ends (twice
as fast) results in 15 min to finish.
ding ding ding...
Me I would use a watch and use the saved rope to
tie up a package for the give away.
What kind of a rope does not burn at a contstant speed?:dropjaw:
The official answer is:
Take rope 1. Lighting it at both ends means that it would take 30 minutes for it to completely burn away. So light rope 1 at both ends and rope 2 at 1 end.
After 30 minutes have elapsed, rope 1 is completely burned through. Rope 2 has 30 minutes of burning remaining, since you know it takes an hour to fully burn.
Light the other end of rope 2 now, and it will take 15 minutes to finish burning since now it's burning from both ends.
Yee Haw!!!!
given was flawed! hanging chads don't count!
Sour grapes eh?Quote:
Originally Posted by hoglahoo
frigg this! I'm going to shave while you burn ropes... :D
Subtle point.Quote:
Originally Posted by Ogershok
it is "Smokey Bear" .... no "the" in the middle.
Officially, that's true. But according to Gene Autry:Quote:
Originally Posted by niftyshaving
Smokey the Bear, Smokey the Bear,
Prowlin' and a growlin', and a sniffin' the air,
He can find a fire before it starts to flame,
That's why they call him Smokey and that's how he got his name.
Did you ever see a forest when a fire was running wild,
And you loved the things within it like a mother loves her child,
Then you'll know why Smokey tells you when he sees you passing through,
Remember please be careful, it's the least that you can do.
Smokey the Bear, Smokey the Bear,
Prowlin' and a growlin', and a sniffin' the air,
He can find a fire before it starts to flame,
That's why they call him Smokey and that's how he got his name.