Numerator: Represents William's total earnings for the week.
Rate for overtime hours: 24, which is the increased rate per hour for overtime.
Earnings when working 50 hours: 1140 for the week.
Numerator:
60: This represents the total amount William earns for the first 40 hours of labor, calculated as his hourly rate multiplied by 40.
24(x-5): This represents the total amount William earns for overtime hours. Here's the breakdown:
24: This is the increased rate per hour William earns for overtime.
(x-5): This represents the number of overtime hours he worked. Since he works 40 hours initially, overtime hours are the total hours (x) minus the initial 40 hours.
Therefore, the numerator of the rational expression represents William's total earnings for the week.
Rate for overtime hours:
The rate at which William is paid for each hour in excess of 40 hours is represented by 24. This is the value directly multiplied by the number of overtime hours in the numerator.
Earnings when working 50 hours:
If William works 50 hours in a week (x = 50), substituting this value into the expression gives:
Numerator: (60 + 24(50-5)) = (60 + 24*45) = 1140
Average hourly rate: (1140 / 50) = 22.8
Therefore, when William works 50 hours in a week, he earns 1140 for the week.