(a)[1]
Amira drives $40$ km to work. She needs $x$ minutes for the first $30$ km. Show that the average speed for the first $30$ km is $\frac{1800}{x}$ km/h.
(b)[3]
Amira’s average speed for the final $10$ km is $\frac{600}{x-25}$ km/h. Her average speed over the first $30$ km is $8$ km/h less than her speed for the final $10$ km. Form an equation in $x$ and show that it reduces to $x^2 + 125x - 5625 = 0$.
(c)[3]
Solve the equation $x^2 + 125x - 5625 = 0$. Show your working and give each solution correct to $1$ decimal place.
(d)[3]
It takes Amira $25$ minutes less to drive the final $10$ km than it does for the first $30$ km. Calculate Amira’s average speed for the whole trip.