A bus is modelled as accelerating uniformly from rest for 12 s, travelling at constant speed for 45 s, and then decelerating uniformly to rest. The magnitude of the deceleration is 32 \dfrac32\,23 times the magnitude of the acceleration. The total distance travelled is 918 m.
Show that the total journey time is 65 s.
Find the greatest speed of the bus.
Explain why the model may underestimate the actual journey time.