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Math Help - Rate Question

  1. #1
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    Rate Question

    Max runs the first 4km of her training session at 8 km/h. At least how many kilometers must she run at 15 km/h in order to average 12 km/h for the whole session.
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  2. #2
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    Hello, begold91!

    Max runs the first 4km of her training session at 8 km/h.
    At least how many kilometers must she run at 15 km/h
    in order to average 12 km/h for the whole session?

    Max ran 4 km at 8 km/hr.
    . . This took \frac{4}{8} \,=\,\frac{1}{2} hours.
    She will run x more km at 15 km/hr.
    . . This will take \frac{x}{15} hours.
    She will run a total of: \frac{1}{2} + \frac{x}{15} hours.

    She will run a total of x + 4 km at an average speed of 12 km/hr.
    . . Her total time will be: \frac{x+4}{12} hours.

    There is our equation! . \frac{1}{2} + \frac{x}{15}\:=\:\frac{x+4}{12}

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  3. #3
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    You could try several equations.

    Since distance/rate=time:

    \frac{4}{8}+\frac{d-4}{15}=\frac{d}{12}, solve for d.

    Since distance = rate*time:

    8(\frac{1}{2})+15(t-\frac{1}{2})=12t, solve for t to find d.
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