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calculus

a road that runs perpendicular to a highway leads to a farmhouse located one mile off the highway an automobile travels down the highway past the road leading to the farmhouse at a speed of 60 mph how fast is the distance between the farmhouse an automobile increasing when the car is 3 miles past the intersection of the highway and the road to the farmhouse

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diego

  1. It would help if you posted your question using proper English, with capitals and periods.....

    At a time of t hours, let the distance of the car past the intersection be x miles.
    let the distance between the car and the farmhouse be d
    I get a simple right-angled triangle with
    sides 1, x and hypotenuse d

    d^2 = 1^2 + x^2
    2d dd/dt = 2x dx/dt
    or dd/dt = x dx/dt /d

    when x = 3
    d^2 = 1 + 9 = 10
    d =√10 , and we are also given that dx/dt = 60

    dd/dt = 3(60)/√10 = 180/√10 = appr 56.9 mph

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    Reiny

  2. if the car is x miles past the road, the distance is

    s^2 = 1+x^2
    when x=3, s=√10

    2s ds/dt = 2x dx/dt
    ds/dt = x/s dx/dt
    when x=3, then,

    ds/dt = 3/√10 * 60 = 18√10 = 56.9 mph

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    Steve

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