Gabriella drives her car 320 miles and averages a certain speed. If the average speed has been 6 miles less she could have traveled only 280

Question

Gabriella drives her car 320 miles and averages a certain speed. If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time. What is her average speed?

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Quinn 2 months 2021-10-15T18:34:11+00:00 1 Answer 0 views 0

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    2021-10-15T18:35:34+00:00

    Answer:

    Her average speed is 48 miles per hour.

    Step-by-step explanation:

    We solve this question using a system of equations.

    The speed equation is:

    s = \frac{d}{t}

    In which s is the speed, d is the distance, and t is the time.

    Gabriella drives her car 320 miles and averages a certain speed.

    So d = 320

    Then

    s = \frac{320}{t}

    If the average speed has been 6 miles less she could have traveled only 280 miles in the same length of time.

    So, which s – 6, d = 280.

    s - 6 = \frac{280}{t}

    From the first equation:

    s = \frac{320}{t}

    st = 320

    t = \frac{320}{s}

    Replacing:

    s - 6 = \frac{280}{t}

    s - 6 = \frac{280}{\frac{320}{s}}

    320(s - 6) = 280s

    320s - 1920 = 280s

    40s = 1920

    s = \frac{1920}{40}

    s = 48

    Her average speed is 48 miles per hour.

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