To find out how many hours Bill worked on the repair, we can set up an equation based on the total bill.
The total bill consists of a fixed scheduling charge and a variable repair charge based on the number of hours worked.
- The fixed scheduling charge is $75.
- The variable cost is $30 per hour, multiplied by the number of hours worked, denoted as \( h \).
The equation for the total bill can be expressed as follows:
\[ \text{Total Bill} = \text{Scheduling Charge} + \text{Hourly Charge} \]
Plugging in the numbers:
\[ 177 = 75 + 30h \]
Next, we can solve for \( h \). First, subtract the scheduling charge from both sides:
\[ 177 - 75 = 30h \] \[ 102 = 30h \]
Now, divide both sides by 30 to find \( h \):
\[ h = \frac{102}{30} \]
Calculating that gives:
\[ h = 3.4 \]
Thus, Bill worked for \( 3.4 \) hours on the repair.
The final answer is:
\[ \boxed{3.4} \text{ hours} \]