Question

Casho is deciding between two parking garages. Garage A charges an initial fee of $12 to park plus $4 per hour. Garage B charges an initial fee of $8 to park plus $6 per hour. Let � A represent the amount Garage A would charge if Casho parks for � t hours, and let � B represent the amount Garage B would charge if Casho parks for � t hours. Write an equation for each situation, in terms of � , t, and determine the interval of hours parked, � , t, for which Garage A is cheaper than Garage B.

Answer 1

For Garage A, the total cost to park for t hours is:

A(t) = 12 + 4t

For Garage B, the total cost to park for t hours is:

B(t) = 8 + 6t

To find the interval of hours parked for which Garage A is cheaper than Garage B, we can set A(t) < B(t) and solve for t:

12 + 4t < 8 + 6t

4t - 6t < 8 - 12

-2t < -4

t > 2

Therefore, Garage A is cheaper than Garage B for any time parked greater than 2 hours.