You can never catch up in a race?

Question

if two runners are placed in a track and the slower runner is given a 100 m lead the faster runner can never catch the slower because he must always come to a point the slower has already passed if both are moving at a constand speed. the fast runner will have run a hundred meters, bringing him to the slowers starting point; during this time, the slower runner has also ran a set distance, say 50 m. it then becomes impossable for the faster to catch the slower, because whenever the fast runner reaches somewhere the slower has been, he still has farther to go :)

Answer 1

If they are both running at a constant speed then one is not a slower runner!!! The faster runner can catch up if he runs faster, how long it takes all depends on their speed relative to each other

Answer 2

This is an exercise in the concept of limits.
A similar story is that: in order to run a mile the runner must first run half a mile then a quarter mile and then an eighth of a mile and so on. IF each of these distances require some time (a finite amount though small), AND the number of distances is infinite, THEN the sum of the infinite number of finite times would be infinite. A runner could never run a mile.
It is well known that a runner can run a mile. The sum of an infinite number of finite numbers can be finite.
Eventually, the faster runner must reach the same point and the same time as the slower runner.

Answer 3

If the velocities remain equal, the runner who started ahead will always be ahead. If the velocities aren't equal, and the second starter is faster, he will eventually catch up with the slower runner that started first. If the opposite is true, the faster runner that started first will simply get farther and farther away.

There is an interesting conundrum here, and that is this: If an immortal person is born, and then 20 years later another immortal is born the first immortal will be infinitely older. After 10 years the older will only be 3 times as old. By 20 years the older will only be 2x as old. By 40 years the older will only be 1.5x as old. If you continue on and on forever, as they are immortal, the fraction by which the older person is older gets smaller and smaller, and eventually approaches 1.0x as old, or the same age. But it never gets there.

This gets into some calculus... that is the assumption that 1/infinity is actually zero, rather than really really close.

So while it would seem that the older immortal will always be 20 years older... over an infinite amount of time they seem to eventually be the same age.


Tiger Striped Dog MD

Answer 4

This conundrum is about 2000 yrs old. Without realizing it, you are simply saying that within a limited time (100m/(difference in speed)) the faster runner cannot catch the slower.
This is fairly obvious to anyone you are trying to convince of the truth of the conclusion that he will NEVER catch the slower runner....

Answer 5

Yep--happens every time you try to use a static method of observation on a dynamic subject. Next time try calculus when you want to describe objects in motion.

(Your observation is only true at a fixed points in time, but the runners are in constant motion. What's true of objects at fixed points in time may have no relevance to objects in motion.)

Answer 6

Nonsense..

Answer 7

This is called Zeno's paradox, and has been around for millenia. Obviously, it does not hold in real life.