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Chase on an endless road, continued


Best Answer gavinksong, 30 July 2013 - 02:58 PM

Spoiler for

Go to the full post


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4 replies to this topic

#1 Rainman

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Posted 30 July 2013 - 01:36 PM

This is a sequel to the puzzle: http://brainden.com/...n-endless-road/

 

You have just managed to catch up to your friend in a race, on a road which goes on forever in both directions. Your friend is a bad loser, and full of adrenaline from the race. "Try and catch me this time", your friend says, and knocks you out cold. When you recover, you have no idea how much time has passed.

  • You move at constant speed x>1 m/s and your friend moves at constant speed 1 m/s.
  • Visibility is limited so you will not be able to see your friend from a distance.
  • You must not stray from the road, same goes for your friend.

Can you catch up to your friend? Does the answer depend on your speed x, and if so, what is the minimum x for which you can catch up? What is your strategy?


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#2 gavinksong

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Posted 30 July 2013 - 02:58 PM   Best Answer

Spoiler for


Edited by gavinksong, 30 July 2013 - 03:06 PM.

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#3 Rainman

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Posted 30 July 2013 - 04:46 PM

Caught again, your friend concedes that you are the supreme runner. Maybe it's not a coincidence that your profile pic is an ostrich ;)


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#4 bonanova

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Posted 31 July 2013 - 02:19 AM

I love this.

 

I didn't do the series to quantify things, so, being lazy I'll just ask:

Do all the questions in the OP have answers?

e.g. if x = 1.0000001, is it impossible? Or just take much longer?


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#5 gavinksong

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Posted 31 July 2013 - 02:33 AM

I love this.

 

I didn't do the series to quantify things, so, being lazy I'll just ask:

Do all the questions in the OP have answers?

e.g. if x = 1.0000001, is it impossible? Or just take much longer?

 

It just takes longer.


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