F.4 variations#######

For the first hour or less, the parking fee $C of a van in car park X is $A. Thereafter, the fee $B varies directly as the parking time on a half-hourly basis. When a van is parked in car park X for 3hours, the parking fee is $68; when a van is parked for 4hours, the parking fee is $92. Assume that a van has been parked in car park X for n hours where n≧1.

(a)
(1) Express B in terms of n.
(2) Express C in terms of n.

(b) If a van has been parked in car park X for 10hours, how much is the parking fee?

(c) For car park Y, the parking fee $F of a van varies directly as the parking time on a half-hourly basis. When a van is parked in car park Y for 6hours, the parking fee is $120. After how long should the van be parked at least such that the parking fee charged by car park X will be higher than that charged by car park Y?