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Math Help - Related Rates Problem

  1. #1
    Junior Member StarlitxSunshine's Avatar
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    Related Rates Problem

    A trough is 15ft long adn 4ft across the top. Its ends are isosceles trianngles with height 3ft. Water runs into the trough at the rate of 2.5 ft^3/min. How fast is the water level rising when it is 2 ft deep?

    [The figure is an upside down triangular prism with the information above & water being "poured in" from a cup]


    Okay...I tried to put down all the information I have:

    the amount of water, lets say "l" -- > l=2ft
    dl/dt is what we're looking for.
    dV/dt = 2.5

    Now I'm supposed to use an equation to figure this out. That's where I'm stuck.
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  2. #2
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    Quote Originally Posted by StarlitxSunshine View Post
    A trough is 15ft long adn 4ft across the top. Its ends are isosceles trianngles with height 3ft. Water runs into the trough at the rate of 2.5 ft^3/min. How fast is the water level rising when it is 2 ft deep?

    [The figure is an upside down triangular prism with the information above & water being "poured in" from a cup]


    Okay...I tried to put down all the information I have:

    the amount of water, lets say "l" -- > l=2ft
    dl/dt is what we're looking for.
    dV/dt = 2.5

    Now I'm supposed to use an equation to figure this out. That's where I'm stuck.
    volume of water in the tank is V = \frac{1}{2} b h \cdot 15

    note also the similar triangles at the end of the trough ...

    \frac{b}{h} = \frac{4}{3}


    get the water volume in terms of h, and then take the derivative w/r to time.
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