(a)[1]
Lara rides at an average speed of $x\text{ km\/h}$. Write down an expression for the number of hours Lara needs to finish the trail.
(b)[4]
Marco cycles at an average speed of $(x-3)\text{ km\/h}$ and takes $15$ minutes longer than Lara. Hence write an equation and show that it simplifies to $x^2 - 3x - 600 = 0$.
(c)[3]
Find the solutions of the equation $x^2 - 3x - 600 = 0$. Show all your working and give your answers correct to $2$ decimal places.
(d)[2]
Determine the time Marco needs to finish the trail. Give your answer in hours and minutes, correct to the nearest minute.