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Related Rates Help please

  1. Feb 4, 2008 #1
    Related Rates Help please!!

    1. The problem statement, all variables and given/known data

    Two cars start moving from teh same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate is the distance between the cars increasing two hours later?"

    2. Relevant equations

    So far I have the equation..
    (z^2) = (x^2) + (y^2)

    I know dy/dt = 60 mi/h and dx/dt = 25 mi/h.

    3. The attempt at a solution

    I implicity differentiated the first equation and ended up with:
    dz/dt = (50x +120y)*(1/2z)

    Since I do not know what x or y is I am unable to find the rate the distance between the two cars is increasing.

    Thank you so much for your help!
  2. jcsd
  3. Feb 4, 2008 #2

    taking the derivative


    You're told that one travels 60 miles per hour and the other, 25 miles per hour. How far would they each have gone after 2 hours?
  4. Feb 4, 2008 #3
    do I multiply the whole equation by 2 then?
  5. Feb 4, 2008 #4
    Not the equation. Read my last sentence!
  6. Feb 4, 2008 #5
    After two hours, they would have gone 120 miles and 50 miles?
  7. Feb 4, 2008 #6
    Correct, now plug those values in. And the rate doesn't change, just the distance.
  8. Feb 4, 2008 #7

    Welcome to the forum AquaGlass.

    Exactly. But how did you get that? Once you figure out that, you will see how to re-express [itex]x[/itex] and [itex]y[/itex].

    Or in other words what are the following proportional to,

    {\frac{dx}{dt}} = {\frac{?}{?}}

    {\frac{dy}{dt}} = {\frac{?}{?}}


  9. Feb 4, 2008 #8
    well then you get Zdz/dt = some number, but what about the Z then.. aren't we trying to find dz/dt? how do you cancel out the z?
  10. Feb 4, 2008 #9
    Use the Pythagorean theorem to find your missing length.

  11. Feb 4, 2008 #10
    ohhh ok i see! thank you so much!!
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