A rectangular tank has a horizontal base. Water is flowing into the tank at a constant rate, and flo

Question

A rectangular tank has a horizontal base. Water is flowing into the tank at a constant rate, and flows out at a rate which is proportional to the depth of water in the tank. At time $t$ seconds the depth of water in the tank is $x$ metres. If the depth is $0.5$m, it remains at this constant value. Show that $\frac{\mathrm{d}x}{\mathrm{d}t}=-k\left( 2x-1 \right)$, where $k$ is a positive constant. When $t=0$, the depth of water in the tank is $0.75$m and is decreasing at a rate of $0.01$ ms$^{-1}$. Find the time at which the depth of water is $0.55$m.

Accepted Answer

$q = 2p; t = 40.2 seconds$

N2001 P2 Q14

N2001 P2 Q14

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