Beach Day by Rodger Bliss
November 2019
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Speed Demons

Andy, Barry, and Carl race each other in a 100-meter dash. They each run at a constant speed throughout the sprint. Andy beats Barry by 20 meters, and Barry beats Carl by 20 meters. How many meters does Andy beat Carl by?

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6 guesses to Speed Demons

  • Nanao Ise

    …This seems to straightforward to be true – but might it be by 40 meters?

  • Dude

    Nope, keep trying.

  • Dude

    Nope, that’s not it. Keep trying.

  • Halim Kim

    36 meters :)

  • Dude

    You are correct, Halim Kim.

    Andy beats Carl by 36 meters.
    It is tempting to guess that Andy beats Carl by 40 meters Nanao Ise, but when Andy finishes and is 20 meters ahead of Barry, Barry is NOT 20 meters ahead of Carl (he’s only 16 meters ahead), and it will take a couple more seconds before Barry increases his lead over Carl to 20 meters.
    To figure out the answer, we let Andy’s speed be A meter/second. So it takes him 100/A seconds to finish the race. At this point, we know that Barry has run 80 meters (since Andy beats him by 20 meters). So Barry runs 80 meters in 100/A seconds, meaning that he is running at a speed of (80/(100/A)) meters/second, or (8A/10) meters per second.
    So we then know that it takes Barry 100/(8A/10) seconds to finish the race, or 125/A seconds. At this point, we know that Carl has run 80 meters (since Barry beats him by 20 meters). So Carl runs 80 meters in 125/A seconds, meaning that he is running at a speed of (80/(125/A)) meters/second, or 80A/125 meters per second.
    Now that we know Carl’s speed, we just need to figure out how far he had run when Andy finished the race. Since Andy finished in 100/A seconds, we can determine that Carl had run (100/A) * (80A/125) = 8000/125 = 64 meters when Andy finished the race. And so Andy beat him by (100 – 64) = 36 meters.

    You are today’s winner.