Question

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.

Answer 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