Math

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A car is heading east toward an intersection at the rate of 40 mph. A truck is heading south, away from the same intersection at the rate of 60 mph. At what rate is the distance between the car and the truck changing when the car is 8 miles from the intersection and the truck is 15 from the intersection?

  • Math -

    let's look at t hrs after the above condition
    let the distance between them be D miles
    then
    D^2 = (40t+8)^2 + (15+60t)^2
    2D dD/dt = 2(40t+8)(40) + 2(15+60t)(60)

    dD/dt = [ 40(40t+8) + 60(15+60t) ]/D

    when t = 0 , the above condition,
    D = √8^2+15^2) = 17
    and
    dD/dt = [ 40(8) + 60(15) ]/17 = 71.76

    At that moment they are separating at 71.8 mph

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