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I'm a simple man living his life and enjoying every moment I get. I don't know much mathematics and I need a little bit of help figuring out the following puzzle.

Today I found out about world champion runner Usain Bolt. He can run 200 meters in 19.19 seconds, which is $10.42\frac{m}{s}$ on average.

I went to track with my buddies and we timed how fast we could run 200 meters. I did 31 second, so my average speed is $6.45\frac{m}{s}$.

Now I've trouble calculating how many meters behind Usain Bolt I would be.

Take a look at these two calculations:

  1. Since I finish 11.81 seconds later and my speed is $6.45\frac{m}{s}$, I'd be 11.81 x 6.45 = 76.17 meters behind.

  2. Since Usain Bolt finishes 11.81 seconds faster and his speed is 10.42m/s, he'd be ahead of me by 10.42 x 11.81 = 123 meters, or in other words, I'd be behind 123 meters and not 76.17 meters.

Which of these calculations is correct and why? They both seem valid to me and I can't figure out why I get two different answers.

bodacydo
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  • Interesting problem! If we assume constant speeds for each of you, then $76.17$ is, to a couple of decimal places, the answer. The constant speeds assumption is not quite right, however. For one thing we have the reaction time to the starter's pistol, also the initial period of acceleration. – André Nicolas Sep 06 '15 at 14:55

1 Answers1

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The first method better reflects what one would understand as how many meters behind you are: You are 76.17 meters behind Bolt at the moment he finishes. At the moment you finally finish, Bolt would be 123 meters ahead. The second distance is larger than the first because it increases over time by the very fact that he is faster than you. Then again, once he has finished he won't keep running for so much longer and at his racing speed; rather you'd run into him still being in the finishing area doing his gesture ...

Hagen von Eitzen
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