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Thread: Rate word problem

  1. March 11th 2010, 03:55 PM #1
    ascendancy523
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    Rate word problem

    So I'm having trouble starting this problem off. (I hate word problems. Well hate is a strong word, I dislike word problems)

    Water is flowing into a balloon at the rate of 20 cc/min. The balloon has a puncture, and the rate at which water flows out of the balloon at this puncture is proportional to the volume of water in the balloon. Let the proportionality constant be 0.07. At what volume do we have equilibrium (that is the volume of water in the balloon remains constant)?

    So far I have \frac{dW_i}{dt}=20 which is water flowing into the balloon and I also have \frac{dW_o}{dt}=0.07V. Any clues where to go from here? Any help is greatly appreciated!
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  2. March 11th 2010, 04:15 PM #2
    skeeter
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    Quote Originally Posted by ascendancy523 View Post

    Water is flowing into a balloon at the rate of 20 cc/min. The balloon has a puncture, and the rate at which water flows out of the balloon at this puncture is proportional to the volume of water in the balloon. Let the proportionality constant be 0.07. At what volume do we have equilibrium (that is the volume of water in the balloon remains constant)?
    \frac{dV}{dt} = 20 - 0.07V

    at equilibrium, \frac{dV}{dt} = 0
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