Calculus

Luke and Leia are trapped inside a trash compactor on the Death Star. The side walls are moving apart at 0.1 m/sec, but the end walls are moving together at 0.3 m/sec. The volume of liquid inside the compactor is 20 cubic meters, a constant. Write an equation expressing the rate of change of depth of the liquid in terms of the width and length of the region inside the compactor.

I only think of
V=wlh=20 .... I'm stuck...can someone please help?
Any help will be appreciated.

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  1. yes
    V = w L h = 20
    dw/dt = .2 m/s
    dL/dt = -.6 m/s

    h = 20/(wL)
    dh/dt = dh/dL dL/dt + dh/dw dw/dt
    dh/dL = -20w/(w^2L^2) = -20/(wL^2)
    dh/dw = -20/(w^2 L)
    so
    dh/dt = [-20/(wL^2)](-.6) +[-20/(w^2L)](.2)
    simplify that

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    posted by Damon

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