## Two Laps

## Two Laps

(OP)

You are going to run exactly two laps of a track. You can run the first lap at any speed you want as long as it's a constant speed. How fast do you need to run the second lap for your total average speed to be twice the speed of the first lap?

Apologies if I didn't describe it clearly. I'll clarify the problem if necessary.

Apologies if I didn't describe it clearly. I'll clarify the problem if necessary.

## RE: Two Laps

## Spoiler:

## RE: Two Laps

## Hidden:

A couple of observations: First, in real life it's impossible to measure speed with infinite precision, so it might be of some interest to calculate just how fast you would have to run in order to get your time on the second lap down to zero, when rounded to the precision of your stop watch. Second, I am not sure why you emphasized that the first lap has to be run at a "constant speed". It seems to me that you would still need to run the second lap instantaneously, regardless of how variable your speed was on the first lap.

## RE: Two Laps

## Spoiler:

Time for first lap = T1

Time for second lap = T2

The average speed of the first lap is: D/T1

The total average speed is: 2D/(T1+T2)

Condition to be met: 2D/(T1+T2)=2D/T1

Simplifying: T1 = T1+T2

T2 must = 0

Therefore the speed of the second lap must be infinity.

## RE: Two Laps

## Hidden:

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What's most important is that you realise ... There is no spoon.

## RE: Two Laps

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advanced cognitive capabilities and other marketing buzzwords explained with sarcastic simplicity

## RE: Two Laps

## Spoiler:

Bye, Olaf.

Olaf Doschke Software Engineering

https://www.doschke.name

## RE: Two Laps

## RE: Two Laps

From a purely mathematical standpoint, infinite speed might be possible, but we live in a physical world that does act weird when relative speeds increase. When speed is approaching the speed of light, there's both dilation of both time and space (we'll discount mass for now assuming we have infinite energy available).

So, the greatest speed we can possibly reach for the second lap is the speed of light. I won't do the math, but even close to the speed of light means you will reach the finish line after a non-zero amount of time.