Bill's Plumbing Service charges $75 to schedule a repair visit plus $30 per hour to make repairs. If the total bill was $177, how many hours did Bill work on the repair?

Question

Express your answer as a decimal number.
Answer

hours

Answer 1

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.

1. The fixed scheduling charge is $75.
2. 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:

$$\boxed{{\displaystyle 3.4}}\text{ hours}$$