If Andrea leaves at $4$ PM, she arrives at the store when it is $5$ PM, and the store closes at $4:30$ PM. If Andrea leaves at $8$ AM, she arrives at the store when it is $9$ AM, and the store opens at $9:30$ AM. 
Andrea needs an hour to get to the shopping center. If she leaves at $4$ PM, she gets there half an hour after the store closes. If she leaves at $8$ AM, she gets there half an hour before the store opens. What hours is the shopping center open? (2007 Math Kangaroo Problem, Level 1-2, Question \#24) 

[A] $7:30$ to $4:30$ 
[B] $8:30$ to $5:30$ 
[C] $7:30$ to $5:30$ 
[D] $8:30$ to $4:30$ 
[E] $9:30$ to $4:30$ 