Math

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A cyclist and a jogger start from a town at the same time and head for a destination 6 mi away. The rate of the cyclist is twice the rate of the jogger. The cyclist arrives 3 hr ahead of the jogger. find the rate of the cyclist.
This is what i got so far but its not adding up.
r t d
cyclist 2x*3=6
jogger x*-3=6

  • Math -

    It always helps to define the variables used, with the units, and cite the equations you use.

    Distance = speed * time, or
    time = distance/speed
    Let
    x=speed of cyclist, m.p.h.
    x/2=speed of jogger, m.p.h.
    D=distance, 6 mi.

    "The cyclist arrives 3 hr ahead of the jogger. find the rate of the cyclist. "
    means that the difference of the time taken by each is 3 hours.
    So we write the equation:
    (D/(x/2) - D/x = 3 hours
    On simplifying,
    D/x = 3 hours
    x=D/3=2 mph (cyclist)
    x/2=2/1=1 mph (jogger)

    Check:
    Time for cyclist: 6/2= 3 hours
    Time for jogger: 6/1=6 hour.
    OK

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