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General discussion (archive)Could anyone help me with this riddle?(23 posts)(23 posts)
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Posted June 06, 2011
I am having some troubles with this riddle I have to solve by tomorrow for my Uni class.

Find the solution for the following: An ant is placed at one end of a rubber string; this rubber string is one kilometer long. The ant starts walking on the string towards the other end with constant speed of one centimeter per second. At the end of each second the string is stretched so its length is extended by additional kilometer.

Here we assume that the string can be stretched indefinitely and that the stretching is uniform. Units of length and time remain constant.

The question is, does the ant ever reach the end of the string?

Thanks a lot, guys!
Post edited June 06, 2011 by barjed
Posted June 06, 2011
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barjed: I am having some troubles with this riddle I have to solve by tomorrow for my Uni class.

Find the solution for the following: An ant is placed at one end of a rubber string; this rubber string is one kilometer long. The ant starts walking on the string towards the other end with constant speed of one centimeter per second. At the end of each second the string is stretched so its length is extended by additional kilometer.

Here we assume that the string can be stretched indefinitely and that the stretching is uniform. Units of length and time remain constant.

The question is, does the ant ever reach the end of the string?

Thanks a lot, guys!
I don't see why he would. Unless I'm missing something, the string becomes 1KM bigger each second, and the ant only moves 1CM per second... 1KM > 1CM.

Unless i'm missing something, which I probably am...
Posted June 06, 2011
... If it takes the ant one second to travel a centimeter, then that means it takes 100 seconds to travel a meter, and 100,000 (100 seconds x 1000) seconds to travel a kilometer.

So by the time the ant has traveled the kilometer, the rubber band is 100,000 kilometers longer.

I say no, but my mind is weird so I might be wrong.
Post edited June 06, 2011 by Foxhack
Posted June 06, 2011
The ant is already on the string's end. The string has two ends. :p
Posted June 06, 2011
He starts at the end of the string, so yes... at least if this is a trick question kind of riddle.

EDIT: Hah, KavazovAngel beat me to it, but not by much!
Post edited June 06, 2011 by adambiser
Posted June 06, 2011
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KavazovAngel: The ant is already on the string's end. The string has two ends. :p
That's a good point. It would be a devious trick if that's what he tried to pull, though.
Posted June 06, 2011
Yes he would eventually reach the end of the string. I'm not going to do the math for you but the key part is "the stretching is uniform". This is of course assuming we're ignoring the lifespan of the ant and assuming that he's immortal.

After each second a small part of the increase is now behind the ant, and the increased amount behind the ant continues to grow with each stretch and constant forward movement of the ant.
Posted June 06, 2011
Nevermind. Missed the uniformly part.
Post edited June 06, 2011 by nondeplumage
Posted June 06, 2011
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Sielle: Yes he would eventually reach the end of the string. I'm not going to do the math for you but the key part is "the stretching is uniform". This is of course assuming we're ignoring the lifespan of the ant and assuming that he's immortal.

After each second a small part of the increase is now behind the ant, and the increased amount behind the ant continues to grow with each stretch and constant forward movement of the ant.
Shoot. That's a good point to.
Posted June 06, 2011
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Sielle: Yes he would eventually reach the end of the string. I'm not going to do the math for you but the key part is "the stretching is uniform". This is of course assuming we're ignoring the lifespan of the ant and assuming that he's immortal.

After each second a small part of the increase is now behind the ant, and the increased amount behind the ant continues to grow with each stretch and constant forward movement of the ant.
Uniform means in both directions by 1000m, or equally 500m on the forward end and 500m on the backward end?
Posted June 06, 2011
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Sielle: Yes he would eventually reach the end of the string. I'm not going to do the math for you but the key part is "the stretching is uniform". This is of course assuming we're ignoring the lifespan of the ant and assuming that he's immortal.

After each second a small part of the increase is now behind the ant, and the increased amount behind the ant continues to grow with each stretch and constant forward movement of the ant.
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KavazovAngel: Uniform means in both directions by 1000m, or equally 500m on the forward end and 500m on the backward end?
It means that the stretch isn't on either end, but evenly throughout the distance.

Take a rubber band, draw a line on it, now pull the rubber band... notice how the increase in length is uniform across the band.
Posted June 06, 2011
So, as I understand it, since the rubber stretches, it stretches the distance traveled by the ant as well and since the ants keeps traveling at a constant pace it's eventually going to reach the end?

edit: Also, wow, fast responses. I guess I have E3 to thank for that :)
Post edited June 06, 2011 by barjed
Posted June 06, 2011
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barjed: So, as I understand it, since the rubber stretches, it stretches the distance traveled by the ant as well and since the ants keeps traveling at a constant pace it's eventually going to reach the end?
Its either that, or what I posted above. Both are correct solutions (assuming I understood Sielle's explanation).
Posted June 06, 2011
Thank you very much for your help guys.
Posted June 06, 2011
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barjed: Thank you very much for your help guys.
Try to present both solutions, for your lecturer to see your way of thinking, depending on the possible desired answer. :)
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General discussion (archive)Could anyone help me with this riddle?(23 posts)(23 posts)
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