The rate of fuel consumption $R$ of a prototype engine, in litres per hour, is modelled by the equation

$$R(t)=\frac{24}{4t+t\sqrt{t}}$$

where $t\ge 1$ is the time in hours since the engine was started. Use algebraic integration and the substitution $u=\sqrt{t}$ to find the total fuel consumed between $t=4$ and $t=16$ hours. Write your answer in the form $12\ln \left(\frac{a}{b}\right)$, where $a$ and $b$ are integers to be found. (Solutions relying entirely on calculator technology are not acceptable.)