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Math Help - Related rates--find time two vehicles are closest

  1. #1
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    Related rates--find time two vehicles are closest

    A truck is 30 km due west of an SUV and is travelling east at a constant speed of 70 km/h. Meanwhile, the SUV is going south at 90 km/h. When will the truck and the SUV be closest to each other?

    I set up a triangle, defined dx/dt as -70t, dy/dt as 90t, and used Pythagorean theorem:

    z^2 = x^2 + y^2

    I then took the derivative of this.
    I'm not sure where to go from here?
    Last edited by jemray; June 23rd 2011 at 03:09 PM.
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  2. #2
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    Re: Related rates--find time two vehicles are closest

    You need to express the distance z (or its square) as a function of t only, take the derivative with respect to t and equate it to zero.
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    Lightbulb Re: Related rates--find time two vehicles are closest

    Thank you, I understand now. I don't know why I found that so confusing.?
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