Solve the differential equation
$$\frac { \mathrm { d } x } { \mathrm {~d} t } = - 2 ( x - 6 ) ^ { \frac { 1 } { 2 } }$$
to find \(t\) in terms of \(x\), given that \(x = 70\) when \(t = 0\).
Liquid fuel is stored in a tank. At time \(t\) minutes, the depth of fuel in the tank is \(x \mathrm {~cm}\). Initially there is a depth of 70 cm of fuel in the tank. There is a tap 6 cm above the bottom of the tank. The flow of fuel out of the tank is modelled by the differential equation
$$\frac { \mathrm { d } x } { \mathrm {~d} t } = - 2 ( x - 6 ) ^ { \frac { 1 } { 2 } }$$
Explain what happens when \(x = 6\).
Find how long it will take for the depth of fuel to fall from 70 cm to 22 cm .