Question

A certain job pays \(\$\)24 per hour for the first 40 hours worked in a week and 1.5 times that rate for any additional hours. If an employee earns \(\$\)1,260 in one week, how many total hours did they work?

• A. 45
• B. 47
• C. 48
• D. 50
• E. 52

Hint:

For overtime pay problems, first calculate the regular earnings, then use the overtime rate for the additional hours to solve for the total time worked.

Answer 1

The Correct Option is C

The employee is paid \(\$\)24 per hour for the first 40 hours, so the earnings for these 40 hours are: \[ 40 \times 24 = 960. \] The total earnings are \(\$\)1,260, so the remaining earnings come from the additional hours worked: \[ 1260 - 960 = 300. \] The rate for the additional hours is 1.5 times the normal rate, or: \[ 1.5 \times 24 = 36 \text{ dollars per hour}. \] Let the number of additional hours worked be \( h \). The earnings from these hours are: \[ h \times 36 = 300. \] Now, solve for \( h \): \[ h = \frac{300}{36} = 8.33. \] Therefore, the total number of hours worked is: \[ 40 + 8.33 = 48 \text{ hours}. \] Thus, the employee worked a total of \( \boxed{48} \) hours.