### Brain Teasers

# Turtle and Rabbit

Rabbit had just lost a race to turtle and had proposed a rematch. Seeing he should have won last time, rabbit wasn't going to make the same mistake. To even the odds, he let turtle have a head start. Turtle was worn out from the last race and was trying to think of an easy way to win. He figured something out and told it to rabbit. Rabbit thought about it and decided he couldn't win because of it. What did turtle say?

### Answer

Turtle told rabbit that to catch up, rabbit would have to run to where turtle started, point A. But by then, turtle would go ahead to point B. By the time rabbit got to point B, turtle would then be at point C, and when rabbit was at C, turtle would be at D, and so on and so on.Hide Answer Show Answer

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## Comments

May 11, 2002

this doesnt make any sense to me cos Rabbit would be making each distance smaller as he was catching up till they tended to zeromeaning the last difference in distance would be cm's and mm's and then zer which is when he would the overtake turtle! ?!?! explai it to me if am wrong

Look, the answer is illogical because in actuality, the rabbit will catch up. BUT...

The distance will get smaller and small but will never reach zero.

The distance will get smaller and small but will never reach zero.

Mogmatt, you're only right IF the rabbit was hopping in increments of one-half. we assume he's not though. so since he's hopping as fast as he can, he WILL eventually catch up to the tortoise.

O.k., In case you missed the whole point of this is that what I described as the answer works out logically, but when you acctualy test it, rabbit WILL catch up. what do you mean by hopping in increments of one-half? Explane And I will hsow you where you are wrong!

oooOOOoooOOO.... big man, big man!

This is one of Zeno's pradoxes which he proposed concerning movement. However, 3 thousand years ago the Calculus and the theory of limits had not been established. It is easy to explain why the rabbit would in fact catch up whether he advances by halves or not. Say Turrtle crawls 100 metres in 10 minutes then his speed is 10 metres per minute. Now he crawls 10 metres in 1 minute. His speed is still 10 metres per minute. Now he crawls 1 metre in 6 seconds (tenth of a minute). His speed is still 10 metres per minute. Turtle is crawling at 10 metres per minute constant speed. You are just choosing to look at smaller and smaller time intervals. As long as rabbit runs faster than 10 metres per second he will catch up and overtake Turtle. It will take 10+1+0.1+0.01...= 11 1/9 minutes. Interestingly you would have glanced an infinite number of times in this 11 1/9 seconds (YES! an infinite number of times in a FINITE time)

I was just about to say that!

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