To find out how many hours Bill worked on the repair, we start by breaking down the total cost into its components, which include the scheduling fee and the hourly repair cost.
The total bill was $177, and the scheduling fee is $75. We can find the total cost of the repairs by subtracting the scheduling fee from the total bill:
\[ \text{Total repairs cost} = \text{Total bill} - \text{Scheduling fee} \] \[ \text{Total repairs cost} = 177 - 75 = 102 \]
Next, we know that Bill charges $30 per hour for the repair work. Let \( h \) represent the number of hours he worked. The cost of the repairs based on the number of hours worked can be expressed as:
\[ \text{Repair cost} = 30h \]
Setting the cost of repairs equal to the total cost of repairs, we have:
\[ 30h = 102 \]
To solve for \( h \), we divide both sides of the equation by 30:
\[ h = \frac{102}{30} \]
Now, calculating \( h \):
\[ h = 3.4 \]
Thus, the number of hours Bill worked on the repair is:
\[ \boxed{3.4} \]