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 $\displaystyle U_{r} $ hours.

(b) Show that, for $\displaystyle 16 \leq r \leq 25 $

$\displaystyle u_{r} = \frac{1}{12}(1.2)^{r-15.} $

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