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Math Help - Lines in a Plane 15

  1. #1
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    Lines in a Plane 15

    You are driving from point A(24,96) on a map grid towards point B with a velocity defined by d=(85,-65) km/h

    a) state the parametric eqtns of the highway line.
    b) how long have you been traveling when you reach a point P 102 km east of where you started at point A?
    c) what are the coordinates of your position P at that time?

    so this is my work below, I need help with parts b and c.

    a) x=24+85t
    y=96-65t

    b) d=AB
    (85,-65)=(x-24)(y-96)
    x-24=85
    x=109
    y-96=-65
    y=31
    |AB|=sqrt (11450)

    (11450)^ (0.5) +102 = 209

    d/s=t
    209/(-65/85)=273 h

    The answer in the back is 55 min

    c) P(194,-34)

    Their answer is (102, 36.4)

    How do I get their answers and what did I do wrong?
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  2. #2
    Eater of Worlds
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    x=24+85t

    Since we are due east, we can use x=102.

    102=24+85t

    t=.917647

    This is hours. Multiply by 60 and get 55.05 minutes.

    part c, y=96-65(.917647)=36.35

    The coordinates are (102, 36.35)

    I think you just had a small mental block. You have the right equations.
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