To determine how many hours the plumber worked, we can divide the total charge by the hourly rate.
The plumber charges $45 per hour and charged Luke $180.
To find the number of hours worked: \[ \text{Hours worked} = \frac{\text{Total charge}}{\text{Hourly rate}} = \frac{180}{45} = 4 \]
So, the plumber worked 4 hours.