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Math Help - ships and related rates

  1. #1
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    ships and related rates

    At noon, ship A is 100 km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing north at 5 km/h. How fast is the distance between the ships changing at 6:00 PM?

    I understand how to do these types of problems, but for this one I can't figure out the right equation to differentiate. Anybody want to point me in the right direction?

    Thanks for the help
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  2. #2
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    Lexington, MA (USA)
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    Hello, Climberboy123!

    At noon, ship a is 100 km west of ship b.
    Ship a is sailing south at 35 km/h and ship b is sailing north at 5 km/h.
    How fast is the distance between the ships changing at 6:00 PM?
    Code:
                              * B
                            * |
                          *   | 5t
                        *     |
        P * - - - - - * - - - * Q
          |         *         :
          |       *           :
      35t |     *             : 35t
          |   *               :
          | *                 :
        A * - - - - - - - - - * R
                   100

    Ship a starts at P and sails south at 35 km/hr,
    . . In t hours, it has sailed 35t km to point A.

    Ship b starts at Q and sails north at 5 km/hr.
    . . In t hours, its has sailed 5t km to point B.

    Note that: . PQ = AR = 100 km.


    Let: x \,=\,AB.

    In right triangle BRA\!:\;\;x^2 \;=\;(40t)^2 + 100^2 \quad\Rightarrow\quad x \;=\;(1600t^2 + 10,\!000)^{\frac{1}{2}}

    Can you finish it now?

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  3. #3
    Newbie
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    Sep 2009
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    thanks! I should be able to get it now.
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