To find out how many hours the plumber worked, we can divide the total charge by the hourly rate.
The plumber charges $45 an hour, and Luke was charged $180.
So, we calculate:
\[ \text{Hours worked} = \frac{\text{Total charge}}{\text{Hourly rate}} = \frac{180}{45} = 4 \]
Thus, the plumber worked 4 hours.
The correct response is 4 hours.