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Hey forum!

In my Precalc class, my teacher loves to give mental stimulation problems before we start our class. The one this week intrigued me, so I wanted to share it with you all! Ready? Let's start!

 

An ant walks on a string that is a foot long. Every second, the ant moves one inch. At the same time, the string gets stretched a foot longer. Assuming that the string never snaps or breaks, will the ant ever get to the end of the string? Also assume that the string is going one direction and doesn't bend around or flip.

 

Good Luck!

BasicMaths

 Nov 15, 2019
 #1
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Here's my take.....

 

The ant never gets to the end of the string

 

Each second, the distance  that the ant covers is   t  inches

 

And each second, the length of the string  (in inches)  =  12  + 12 t

 

So.....the ratio of the distance that the ant has traveled in t seconds  to the string length at that time is just

 

        t

________

12 t  +  12

 

As  t approaches some infinite number of seconds, this ratio   converges  to

 

       t                   1

_______  =      ____

   12 t                  12

 

Therefore, the ant can never travel much more than 1/12  the string length  as t approaches infinity

 

 

cool cool cool

 Nov 15, 2019
 #2
avatar+58 
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CPhill, that's a very intuitive guess!

However, there's one factor you haven't taken into account. Try to see if you can find it :)

 Nov 15, 2019
 #3
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I can't fint it either.

I checked it with calculus but the problem appears straight forward.

What are we missing?

Melody  Nov 15, 2019
 #4
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Whatever.....spoiler alert....the ant dies in the end.....!!!!

 

 

cool cool cool

CPhill  Nov 15, 2019
 #5
avatar+106037 
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Yea and they lied about that string too.

It didn't break exactly it just deteriorated with age and fell to bits. That is when the ant plunged to its death!

Melody  Nov 15, 2019
 #6
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Does the string elongate in only one direction?  If so, is the ant required to crawl that direction, or can the ant turn around and go to the static end?

 Nov 16, 2019
 #7
avatar+58 
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This thread is comedy GOLD! 😂 Anyways, I'll tell you the thing you were missing. When the string stretches, the point the ant was on moves with it. So in theory, the ant will travel a little more than an inch and will eventually overtake the string! You can even view this in Desmos for all you visual learners.......at least that's what my teacher did! 😂 But most people do actually think that way; the ratio will always stay constant; but you must think outside the box for this one!

 

Good job everyone!

BasicMaths

 Nov 16, 2019
 #8
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ok BM I like that.

That is worth thinking about :)

Melody  Nov 16, 2019
 #9
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It would depend on how the sting is getting streched. 

As guest commented, if it is getting streched sideways it would make no difference.  If it was getting streched from the back and the front stayed put then the ant is going backwards i think.

If from both ends then I think the ant would probably keep going backways.  

Only if it is getting streched in a forward direction will it add to the ants progress.

 

It would have been good if you had added in the address of your teachers desmos display.

Melody  Nov 16, 2019
 #10
avatar+58 
+1

Yeah, but unfortunately, I couldn't access my teachers laptop; I should have asked him .-.

 Nov 16, 2019
edited by BasicMaths  Nov 16, 2019
 #11
avatar+106037 
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He could have just sent the whole class the address of it.

It is easy to do that with Desmos.

Melody  Nov 16, 2019

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