On Monday, Ravi goes for a $20\text{ km}$ run. His mean speed over the first $12\text{ km}$ is $x\text{ km/h}$. Write down an expression, in terms of $x$, for the time taken to cover the first $12\text{ km}$. Give your answer in minutes.
His mean speed for the final $8\text{ km}$ of the run is $1.5\text{ km/h}$ less than it was for the first $12\text{ km}$. Write an expression, in terms of $x$, for the time taken to cover the final $8\text{ km}$. Give your answer in minutes.
Ravi takes $110$ minutes to complete the full $20\text{ km}$. Form an equation in $x$ and show that it simplifies to $22x^2 - 273x + 216 = 0$.
Solve the equation $22x^2 - 273x + 216 = 0$. Show all working and give each answer correct to 2 decimal places.
On Friday, Ravi completed the whole $20\text{ km}$ at the same mean speed as the speed he kept for the final $8\text{ km}$ on Monday. Calculate the time Ravi took to run $20\text{ km}$ on Friday. Give your answer in hours and minutes, correct to the nearest minute.