F.4 variations#######

2010-01-30 3:00 am

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?

回答 (1)

用戶9112

2010-01-30 7:50 pm

✔ 最佳答案

B = k(n-1)/2 where k is a constant
C = A + k(n-1)/2
68 = A + k
92 = A + 1.5k
24 = 0.5k
k = 48 => A = 20
(1) B = 24(n-1) = 24n – 24

C = 20 + 24(n-1) = 24n – 4
(b) Parking fee for 10 hours = 24*10 – 4 = $236
(c) Parking fee for Y, F = pn/2 where p is a constant
120 = p*6/2 => p = 40
Hence F = 20n
For C > F => 24n – 4 > 20n
4n > 4
n > 1
Therefore the minimum time is one and a half hour.

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