Answer: To calculate the man's gross pay for the week, we need to consider both his regular hours and overtime hours.
Regular hours: The man worked 45 hours in total, and any hours up to 40 are considered regular hours since he earns $16.10 per hour for them.
Overtime hours: Any hours worked beyond 40 are considered overtime hours, and he gets time and a half for these hours. So, the overtime pay rate is 1.5 * $16.10 = $24.15 per hour.
Now, let's calculate the gross pay:
Regular pay = 40 hours * $16.10 per hour = $644.00
Overtime pay = (45 hours - 40 hours) * $24.15 per hour = 5 hours * $24.15 = $120.75
Gross pay for the week = Regular pay + Overtime pay
Gross pay for the week = $644.00 + $120.75 = $764.75
The man's gross pay for the week is $764.75.