A parking garage charges $K for the first hour or fraction of an hour and $2/3K for each hour thereafter. Bill parked 7 times as long as Ray. If Ray parked for 1/2 hour, Bill paid _____ times as much as Ray.
3
Ray paid $K for 1/2 hour
Bill needs to pay for 7(1/2 hour)
Bill paid $K + 2.5(2/3K)
To solve this problem, we need to determine how long Bill parked and then calculate the amount he paid by applying the given charges.
Let's start by calculating how long Bill parked. We are told that Bill parked 7 times as long as Ray, and Ray parked for 1/2 hour. So, we can determine Bill's parking duration by multiplying Ray's parking time by 7:
Bill's parking time = 7 * Ray's parking time = 7 * 1/2 hour = 7/2 hours or 3.5 hours.
Now that we know how long Bill parked, we can calculate the amount he paid using the given charges. The parking garage charges $K for the first hour or fraction of an hour, and $2/3K for each hour thereafter.
First, let's calculate the cost for the first hour or fraction of an hour:
Cost for the first hour or fraction of an hour = 1 * K = K.
Next, let's calculate the cost for each additional hour beyond the first hour:
Cost for additional hours = (Number of additional hours) * ($2/3K per hour) = (3.5 hours - 1 hour) * ($2/3K per hour) = 2.5 * ($2/3K) = 5/3 * ($2/3K) = (10/9)K.
Finally, let's calculate the total amount Bill paid:
Total amount Bill paid = Cost for the first hour or fraction of an hour + Cost for additional hours = K + (10/9)K = (19/9)K.
So, Bill paid (19/9) times more than Ray, or approximately 2.11 times more than Ray since K is undefined.