Riddle

There is a rabbit and a turttle.They decide to make a race. The generous rabbit allows the turttle to start first since he is 10 times faster. After some time the turttle has covered D meters,feet or whatever it doesn t matter


By the time the rabbit will cover D the turttle will cover D/10 and by the time the rabbit will cover the rest D/10 the turttle will have covered another D/100 and by the time the rabbit catches that 2 the turttlr will be ahead D/1000...

Therefore...

It s impossible for the fast rabbit to reach the slow turttle!

 

You can t do that it s duck's seasson...

[video=youtube;9-k5J4RxQdE]http/www.youtube.com/watch?v=9-k5J4RxQdE[/video]

later that day...
[video=youtube;1G8Xlx7dfT8]http/www.youtube.com/watch?v=1G8Xlx7dfT8&NR=1[/video]

and finally ... things go how it should be
[video=youtube;7syAkQmc-lM]http/www.youtube.com/watch?v=7syAkQmc-lM&NR=1[/video]

 

after 11 units of time, the rabbit would be ahead of the turtle. Your argument is invalid.
Here is the proof:
Let' the turtle's speed be 1 m/sec and the rabbit's speed be 0 m/sec for the first 10 seconds of the race
After 10 seconds, the rabbit's speed becomes 10 m/sec
In 11 seconds, the turtle has traveled 11 m and the rabbit has traveled 10 m.
The turtle is ahead of the rabbit.
After 12 seconds, the turtle would have traveled 12 m and the rabbit would have traveled 20 m.
The rabbit will ultimately win the race.

 

Ofc it s invalid that s not the issue... We know from experience that this is not correct and ur simple example proves it...

But u didn t tell us where is the error of the paradox arguement.

 

Your paradox argument is flawed, in that it takes a fact (it will take the rabbit 10% longer to catch up to the turtle) and confabulates it (D/10, D/100, D/1000) in an attempt to confuse the reader.

By the way, I am defining D as the distance the turtle travels BEFORE the rabbit starts running.
If, by the time the rabbit covers a distance (10m) the turtle would have covered an extra 10m/10 (or 1m) the turtle still has the upper hand. If the rabbit waited until the turtle covered 100m, then the turtle would have covered 100m/10, or 10m. All this means is that, as D increases (distance turtle travels before rabbit starts race), the amount of time the rabbit will need to catch up will increase at 10% that rate. (turtle covers 100m in 100 sec, rabbit takes 10 secs to catch up, turtle is now only 10m ahead, after 1 more second, rabbit will have caught up to turtle. Total time elapsed is 100 sec +10%).

If the turtle can complete more than 90% of the race before the rabbit begins, the turtle will win, but if it completes any less than 90%, it is impossible for it to win.

 

The paradox is flawed!! that s what a paradox is however there is no trick here nor attempts to confuse the reader. And u offer no refutation with what u say and no matter how many examples u bring u ll have no refutation. This is a mathematical paradox and the refutation lies in limit theory.

 

The paradox is flawed.

If D is defined as the distance that the turtle travels before the rabbit begins racing, then if the finish line is at any distance less than D (D/10, D/100, D/1000) the turtle will win the race because IT WOULD HAVE ALREADY PASSED THE FINISH LINE! This is no paradox, you are not even understanding your own words!

 

Who said anything about a finish line ? there is no finish line if the rabbit passes the turtle it wins...unfortunatelly according to limit theory the rabbit can never pass the turtle as i have proven...

U allready have proven that the rabbit will pass the turtle in X seconds according to time given as headstart (allthough u didn t provide us with an equalization) that was correct
However ur analysis lacks 2 things

U haven t told us at what distance (in terms of D) the rabbit will reach the turtle
And u haven t provide us with a rule that refutes my theory

and u cannot do either and that s the paradox

 

The distance necessary for the rabbit to pass the turtle is 1.1*D

The rule is already stated.
So long as the distance to the finish line is greater than 1.1*D the rabbit will always win. Anything less, the turtle wins. If the finish line is an infinite distance away, the rabbit will inevitably win (after an infinite amount of time) regardless of what D is. (D must be a real number)