Will he ever catch the turtle?

[VERTEX]

Imagine a situation where an individual could run at a speed 10 times faster than a turtle.

In a race situation, the runner gives the turtle a 100m head start.

The race begins and the runner runs the 100m, while the turtle runs 10m, the runner runs the 10m while the turtle runs 1m, the runner runs 1m while the turtle runs 1/10m, etc etc ad infinitum.

Will the runner ever catch the turtle?

If yes why, if no why?

Good luck.

[AquaShrimp]

No, the turtle will always be one step ahead of the runner.

[Meatwad]

Yes because the turtle will become roadkill when it tries to cross the road.

[midnight Target]

Didn't Zeno have something to say about this?

http://en.wikipedia.org/wiki/Zeno's_paradoxes#Achilles_and_the_tortoise

[VERTEX]

Originally posted by midnight Target
Didn't Zeno have something to say about this?

1 point for midnight target,

anyone care to answer the question seriously?

[Furball]

They would run until the runner goes all the way round the world, and then as the runner goes past the turtle he can bite him in the arse.  Turtle 1 Man 0.

My other answer would be, depends if he is a Teenage Mutant Ninja Turtle, in which case he will just nunchuck the man before the race starts... QUAH!

[mietla]

A sum of the infinite series does not have to be infinite.

[lasersailor184]

Originally posted by VERTEX
1 point for midnight target,

anyone care to answer the question seriously?

It's a mathematical limits problem.



If you first analyze it logically (asking a greek philosopher to do that is often very hard) you would set the speeds constant.  This becomes a simple Distance versus Time problem.  Where you figure out the speed and position of the turtle in a simple equation.

x= Distance, T = time.  

So for the Turtle, X = T + 100.  Meaning that the position of the turtle is it's speed (actually 1 x T) times the amount of Time spent, plus the initial 100 meters.  

For the rabbit, the equation would be X = 10T + 0 .  0 meaning he starts at 0 while the turtle is 100 yards ahead.

Then when you assume that at some time T they will be in the same position X, you can make the equation "T + 100 = 10T".  Solve for T, and you get 11 and 1/9 seconds til the Rabbit overtakes the turtle.

However (continued in next post)

[VERTEX]

10 points for lasersailor, thanks for the insight

[lasersailor184]

However, when you make the speed of the rabbit a function of how far the Turtle has traveled, it becomes a limit equation where the function of the Rabbits' position approaches and comes infinitely close, but never touches the equation of the line of the Turtle's position.

This is where I get rusty.


The equation of the Rabbit's position vs. time can be graphed on an XY coordinate, merely Substituting Y for X, and X for T.  The distance traveled will be actually represented on Y height, and X represents time.

So the equation for the Turtle becomes Y = X + 100.  It is a simple line equation.

I believe that you would equation would be some function of Natural Log, but how to get it, I can't remember at all.

[USRanger]

[Speed55]

I don't understand the complexity of the problem.
In the question, it doesn't say the distance of the race, so given enough time the individual will definitely overtake the turtle.

[FrodeMk3]

Originally posted by VERTEX
Imagine a situation where an individual could run at a speed 10 times faster than a turtle.

In a race situation, the runner gives the turtle a 100m head start.

The race begins and the runner runs the 100m, while the turtle runs 10m, the runner runs the 10m while the turtle runs 1m, the runner runs 1m while the turtle runs 1/10m, etc etc ad infinitum.

Will the runner ever catch the turtle?

If yes why, if no why?

Good luck.

Is it an African, or a European Turtle?????

(Insert Pic of VERTEX flying into the Chasm of Doom)

[Latrobe]

Originally posted by VERTEX
anyone care to answer the question seriously?

Us? Seriously?

[lasersailor184]

Originally posted by Speed55
I don't understand the complexity of the problem.
In the question, it doesn't say the distance of the race, so given enough time the individual will definitely overtake the turtle.

Think of it in a Car Chase sort of way.  To catch the criminal, the cop has to go faster then the other car.  But if the cop continues to go as fast as before, he'll overshoot the car.


So as the cop gets closer, he starts to match the speed of the chase car, until some indefinite time down the road the Cop is a foot behind the runner, and they are both going the same speed.