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Math Help - Related rate problem

  1. #1
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    Related rate problem

    Since this forum was so helpful on my last question I have another one I'm struggling with.....

    Phoebe is going east on Alamo street at 40 ft./second, meanwhile Calvin is going south on heights street at 30 ft./second. We need to determine the straight line distance between them. Then, when Phoebe is 200 feet from the intersection, Calvin is 600 ft. from the intersection. At this time is the straight-line distance between them increasing or decreasing? At what rate?

    Thanks!
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  2. #2
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    The question appears to be ambiguous. How do we know whether Calvin and Phoebe are approaching or leaving the intersection?

    At any rate, if s_C represents Calvin's distance from the intersection and s_P represents Phoebe's distance, we are given that

    \begin{aligned}<br />
\frac{ds_C}{dt}&=\pm 30\\<br />
\frac{ds_P}{dt}&=\pm 40.<br />
\end{aligned}<br />
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  3. #3
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    Quote Originally Posted by wismadison2010 View Post
    Since this forum was so helpful on my last question I have another one I'm struggling with.....

    Phoebe is going east on Alamo street at 40 ft./second, meanwhile Calvin is going south on heights street at 30 ft./second. We need to determine the straight line distance between them. Then, when Phoebe is 200 feet from the intersection, Calvin is 600 ft. from the intersection. At this time is the straight-line distance between them increasing or decreasing? At what rate?

    Thanks!
    If Calvin is NORTH of the intersection then the distance between Calvin & Phoebe is DECREASING.

    If Calvin is SOUTH of the intersection then the distance between Calvin & Phoebe is INCREASING.

    Do you need all cases?
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