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Math Help - related rates help!!!

  1. #1
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    related rates help!!!

    At noon, ship A is 125 km east of ship B. Ship A is sailing west at 35 , and ship B is sailing north at 35 . How fast is the distance between the ships changing at 2:00 P.M. in ?
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  2. #2
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    Hello, singh!

    At noon, ship A is 125 km east of ship B.
    Ship A is sailing west at 35 km/hr, and ship B is sailing north at 35 km/hr.
    How fast is the distance between the ships changing at 2:00 P.M.?

    I hope you made a sketch . . .
    Code:
        B *
          | \
          |   \
          |     \
      35t |       \  x
          |         \
          |           \
          |             \
          * - - - - - - - * - - - - - - *
          Q    125-35t    A     35t     P
          : - - - - - - 125 - - - - - - :

    At noon, ship A is at point P.
    In t hours, it has moved 35t km to point A.
    Then: AP \:=\:x, and QA \:=\:125-35t

    At noon, ship B is at point Q.
    In t hours, it has moved 35t km to point B.

    Their distance is: . x \;=\;\sqrt{(125-35t)^2 + (35t)^2}

    So we have: . x \;=\;\left(2450t^2 - 8750t + 15,625)^{\frac{1}{2}}

    Can you finish the problem?

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  3. #3
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    not sure what your asking?

    not sure what your asking? are you asking final distance between the 2 ships?

    d=r(t)
    distance= rate(km/hr) X time from noon to 2pm is 2 hrs
    70km= 35km/hr x 2 hrs

    the distance is the hypothnuse of the open triangle below. use pythrugrams therom to solve for it. a^2+b^2=c^2



    . l
    . l70km
    . l
    ---70km--A--125km---B
    195km
    Last edited by poofighter; November 15th 2007 at 05:41 PM. Reason: editor is messing up triangle \ignore periods in new version
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  4. #4
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    thanks...that helps a lot. but one question. does the part about the rate of change of distance at 2 PM have no relavence to the problem? does it matter whether they ask how fast is the distance changing at 2 PM, 3 PM, 4PM and so on??
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