calculus

One bicycle is east of an intersection , and it is travelling towards the intersection of 9 miles per hour. at the same time a second bicycle is south of the intersection , and it is travelling away from the intersection at the rate of 10 miles per hour. Is the distance between the bicycles increasing or decreasing when the first is 4 miles east and the second is 4 miles south of the intersection? at what rate?

asked by uGinn
  1. let u be the distance of the first bike
    let v be the distance of the second bike

    u^2+v^2=x^2
    given du/dt=-9
    and dv/dt=10

    2x dx/dt=2u du/dt + 2v dv/dt
    dx/dt= (u du/dt +v dv/dt)/x
    now solve for dx/dt when u=4,v=4, and du/dt and dv/dt given as above.
    if it is increasing, dx/dt will be +

    posted by bobpursley
  2. e = distance east
    s = distance south
    h = hypotenuse, what we want

    at start
    e = 4
    s = 4
    de/dt = -9
    ds/dt = +10
    h = 4 sqrt 2

    h^2 = e^2 + s^2
    2 h dh/dt = 2 e de/dt + 2 s ds/dt

    4 sqrt 2 (dh/dt) = 4 (-9) + 4 (+10)

    sqrt 2 (dh/dt) = +1
    dh/dt = 1/sqrt 2 = +.707 miles/hour

    obviously 10 is bigger than 9 :)

    posted by Anonymous

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