Final answer:
Lizzie's hourly overtime rate is $67.50.
Step-by-step explanation:
To find the hourly overtime rate, we first need to determine the total number of overtime hours worked. In this case, Lizzie worked a total of 47 hours, which is 7 hours more than her regular 40-hour week.
Next, we need to calculate how much extra Lizzie would earn for each hour of overtime. Since she receives time-and-a-half pay, her overtime rate is 1.5 times her regular hourly rate of $45. Therefore, her hourly overtime rate is $45 imes 1.5 = $67.50.