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Other related rates problem

  1. Nov 12, 2004 #1
    Water is being pumped into a trough that is 4.5m long and has a cross section in the shape of an equilateral triangle 1.5m on a side. If the rate of inflow is 2m3/min, how fast is the water level rising when the water is 0.5m deep?

    Answer is 0.77m/min.

    Sorry for not posting this in the homework help section - saw the sign afterwards, and don't really have much time to move it.
  2. jcsd
  3. Nov 15, 2004 #2


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    Another point is that you should show us what you have already tried- don't just post the problem!
  4. Nov 15, 2004 #3
    Well, I can try to help you, but I don't have enough time to work it out.

    You want to find the rate of change of the area, so you'll need to use


    Then eventually differentiate.

    You should use properties of similar triangles to solve for the unknown.


    and you should be able to know all those variables.

    Or else I'm completely wrong
  5. Nov 16, 2004 #4
    But its a triangular prism, isn't it? I don't think just using area will work. I did this:

    I use the equilateral triangle to find the height of the prism, and used the equation:

    V = 1/2lwh (where l is 4.5, height is 1.5, and width was solved in terms of h).
    = 1/2lo.58h^2, (er something like that)
    I tried differentiating the equation to get:
    dv/dt = 1.16h(dh/dt) --> (i think)

    My final answer was 0.75m/min
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