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Math Help - work check: related rates

  1. #1
    Junior Member
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    work check: related rates

    2 cars move from same point. one travels north 28mi/hr and the other travels east 70mi/hr

    a) write an equation to relate these variables

    i did dz/dt = x*dx/dt + y*dy/dt * 1/z

    b) at what rate is the distance between the cars increasing 5 hours later?

    so z^2 = x^2 + y^2
    5*28 = 140
    5*70 = 350
    z = sqrt(142100)

    dz/dt = (140*28 + 350*70)/ 376.96
    dz/dt ~= 75.39

    did i work it out and calculate correctly?

    the problems i'm working w/ don't have an answer key and i'm wondering if this is the right answer as well as proper process to go about a problem like this
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  2. #2
    MHF Contributor
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    Both answers are correct. Maybe your z^2 = x^2 + y^2 is more to the point of part a, and notice (maybe it's a trick question to make this point) that the rate of separation doesn't depend on t
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