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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

    HallsofIvy

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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

    a=1/2bh

    Then eventually differentiate.

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

    then,
    da/dt=(1/2)bh*(db/dt)

    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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