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Math Help - Related rates help again

  1. #1
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    Unhappy Related rates help again

    A ship is 15 miles east of O and moving west at 20mph; ship B is moving 60miles south of O and moving north at 15mph. Are they approaching or separating after 1 hour and at what rate?
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  2. #2
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    Hello, ^_^Engineer_Adam^_^!

    Ship A is 15 miles east of O and moving west at 20 mph;
    ship B is 60 miles south of O and moving north at 15 mph.
    Are they approaching or separating after 1 hour and at what rate?
    Code:
              :     15-20t      A    20t    P
          - O * - - - - - - - - * - - - - - * - -
              |              *
              |           *
       60-15t |        * x
              |     *
              |  *
            B *
              |
          15t |
              |
            Q *

    Ship A starts at point P, 15 miles east of O.
    . . In t hours, it has traveled 20t miles west to point A.
    . . Hence: OA = 15 - 20t

    Ship B starts at point Q, 60 miles south of O.
    . . In t hours, it has traveled 15t miles north to point B.
    . . Hence: OB - 60 - 15t


    Let x = AB.

    From Pythagorus, we have: .x .= .(15 - 20t) + (60 - 15t)

    . . which simplifies to: .x .= .625t - 2400t + 3825 .[1]


    Differentiate with respect to time: . 2x(dx/dt) .= .1250t - 2400

    . . and we have: .dx/dt .= .25(25t - 48)/x .[2]


    When t = 1, [1] gives us: .x .= .625 - 2400 + 3825 .= .2050 . . x .= .5√82


    Substitute into [2]: .dx/dt . = . 25(25 - 48)/(5√82) . = . -12.6996255
    . . The distance is decreasing.


    Therefore, they are approaching at about 12.7 mph.

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