To calculate the gross pay for a 45-hour work week, we need to break it down into regular hours and overtime hours.

1. Regular Pay: The employee gets paid $12.60 per hour for up to 40 hours. So, the regular pay for the first 40 hours is: $40 \, \text{hours} \times 12.60 = 504 \, \text{dollars}$

2. Overtime Pay: Any hours worked over 40 are paid at time-and-a-half (1.5 times the regular hourly rate). The employee worked 45 hours, so they worked 5 overtime hours: $\text{Overtime rate} = 12.60 \times 1.5 = 18.90 \, \text{per hour}$ The pay for the 5 overtime hours is: $5 \, \text{hours} \times 18.90 = 94.50 \, \text{dollars}$

3. Total Gross Pay: Now, add the regular pay and the overtime pay together: $504 + 94.50 = 598.50 \, \text{dollars}$

Thus, the employee's gross pay for a 45-hour work week is $598.50.

Would you like further details on how to calculate pay or any other clarification? Here are 5 related questions:

1. What if the employee worked 50 hours in the same week, how would the gross pay change?
2. How do you calculate overtime for different types of work agreements?
3. What are the common labor laws regarding overtime pay?
4. How is gross pay different from net pay?
5. Can an employee request time off instead of overtime?

Tip: Always remember to confirm the local labor laws for overtime pay, as they may vary by region or company policy.