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Math Help - related rates, water running into trough

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    related rates, water running into trough

    Water is running into a trough at rate 2 ft^3 / min. The cross section of the trough is an isosceles trapezoid with two bases 5 ft and 11 ft and a height of 4 ft. The length of the trough is 20 ft. How fast is the water level rising one hour later?

    so i have the equation V = (1/2) h (b1 + b2) 20 = 10 (h) (b1 + b2), i drew the trapezoid so that the smaller base is on top and since water is filling the trough, the bottom base won't be changing so my volume equation is now V = 10 (h) (b1 + 11). since i am given dV/dt and i need to find dh/dt, i need to somehow get rid of b1 and express it in terms of h. that's where i'm stuck at. how do i express b1 in terms of h. do i have to use similar triangles? if so, which triangles do i use?
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    Quote Originally Posted by oblixps View Post
    Water is running into a trough at rate 2 ft^3 / min. The cross section of the trough is an isosceles trapezoid with two bases 5 ft and 11 ft and a height of 4 ft. The length of the trough is 20 ft. How fast is the water level rising one hour later?

    so i have the equation V = (1/2) h (b1 + b2) 20 = 10 (h) (b1 + b2), i drew the trapezoid so that the smaller base is on top and since water is filling the trough, the bottom base won't be changing so my volume equation is now V = 10 (h) (b1 + 11). since i am given dV/dt and i need to find dh/dt, i need to somehow get rid of b1 and express it in terms of h. that's where i'm stuck at. how do i express b1 in terms of h. do i have to use similar triangles? if so, which triangles do i use?
    the 3-4-5 triangles on both end sides of the trapezoid.


    trapezoidal cross-section of water in the trough ...

    upper base = 5+2x

    lower base = 5

    height = h

    relationship between x and h ... \frac{x}{h} = \frac{3}{4}

    x = \frac{3h}{4}

    area of the trapezoidal cross-section of water ...

    A = \frac{h}{2}\left[(5+2x) + 5\right]

    A = \frac{h}{2}\left[\left(5+ \frac{3h}{2}\right) + 5\right]

    can you take it from here?
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