A competitor is running in a 25 km race. For the first 15 km, she runs at a steady rate of 12 km h-1. After completing 15 km, she slows down and it is now observed that she takes 20% longer to complete each kilometre than she took to complete the previous kilometre.

(a) Find the time, in hours and minutes, the competitor takes to complete the first 16 km of the race.

The time taken to complete the rth kilometre is

hours.

(b) Show that, for

(c) Using the answer to (b), or otherwise, find the time, to the nearest minute, that she takes to complete the race.