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Math Help - Related Rates problem...

  1. #1
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    Related Rates problem...

    A racer can cycle around a circular loop at the rate of 3 revolutions per hour. Another cyclist can cycle the same loop at the rate of 5 revolutions per hour. If they start at the same time (t=0), at what first time are they farthest apart?
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    Quote Originally Posted by derekjonathon View Post
    A racer can cycle around a circular loop at the rate of 3 revolutions per hour. Another cyclist can cycle the same loop at the rate of 5 revolutions per hour. If they start at the same time (t=0), at what first time are they farthest apart?
    s = r \cdot \theta

    for cyclist 1, \theta_1 = 6\pi t

    for cyclist 2, \theta_2 = 10\pi t

    s_2 - s_1 = r(10\pi t - 6\pi t) = r(4\pi t)

    farthest distance will be when they are half a circumference apart ( \pi r) ...

    t = \frac{1}{4} hr
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