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Rate of Change (Rectangle)

  1. Nov 23, 2008 #1
    1. The problem statement, all variables and given/known data
    A rectangle has a constant area of 200m2 and its length L is increasing at the rate of 4 meters per second. Find the width W at the instant the width is decreasing at the rate of 0.5 meters per second.

    2. Relevant equations
    [tex]dA/dt =0[/tex] (since the area is constant)
    [tex]dL/dt =4 m/s[/tex]
    [tex]dW/dt =-0.5 m/s[/tex]
    and I'm not sure, but parameter is [tex]P=2L+2W[/tex]

    3. The attempt at a solution
    I wrote L in terms of W, and W in terms of L, but I am having trouble taking L=(200/W) to dL/dt.
    I know that most related rates problems need two equations, so I have been trying to figure out how parameters may work in. Any help is greatly appreciated.
    Last edited: Nov 23, 2008
  2. jcsd
  3. Nov 23, 2008 #2
    This is true at only one point in time, not as an identity. You first want to know the rate of change of W. Certainly, W=A/L, so

    For what value of L is this equal to .5? What is the corresponding value of W?
  4. Nov 23, 2008 #3
    Ahhhhh, I understand now!
    My problem was just that, I thought that dW/dt=-.5 all the time, I forgot its connection to L! Thank you very much for your assistance.
  5. Oct 18, 2009 #4
    I'm sorry to bring this up again, but I have the same problem on a packet. I understand that dW/dt does not equal .5 all the time.

    However, I don't see the reasoning behind "certainly, w = a/l, so..." and then the little graphic. Could someone explain it to me?
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