Algebra

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During the race, Bernie ran 9 meters every 4 seconds, while Barnaby ran 2 meters evey second and got a 10 meter head start. If the race is 70 meters long, did Bernie ever catch with Barnaby? If so, when?

I have to use a proportion to solve this.

  • Algebra -

    The proportion can be the speed: 9/4 = 2.25 m/s for Bernie and 20.00 m/s for Barnaby.

    The distance from the starting line at time t after the start is
    X1 (Barnaby) = 10 + 2 t
    X2 (Benie) = 2.25 t
    Bernie passes Barnaby when X1 = X2. Solve for the X where that happens.
    10 + 2t = 2.25 t
    10 = 0.25 t
    t = 40 seconds

    X1 = X2 = 90 m

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