Question

An electrician charges $60 as a one-time fee plus an additional $55 per hour. If the total bill is $252.50, how many hours did it take for the electrician to complete the repair? Part A: Define the variable for this problem. (5 pts)

Answer 1

Part B: Write an equation with the variable to represent the situation. (5 pts)

Answer 2

Part C: Solve the equation using inverse operations. Show ALL work

Answer 3

Part D: If he arrived at 10:30 a.m., what time was he finished with the repair? Show calculations. (5 pts)

Answer 4

Part A:

Let \( h \) represent the number of hours the electrician worked.

Now the total cost can be expressed with the following equation based on the given charges:

Total bill = One-time fee + (Hourly rate × Number of hours)
\[
\text{Total bill} = 60 + 55h
\]

In this problem, the total bill is $252.50, so we can write the equation as:
\[
252.50 = 60 + 55h
\]

Thus, the variable defined for this problem is \( h \), the number of hours worked by the electrician.

Answer 5

Part B:

Based on the situation described, the equation that represents the total bill for the electrician's services can be written as:

\[
252.50 = 60 + 55h
\]

In this equation:
- \( 252.50 \) is the total bill,
- \( 60 \) is the one-time fee,
- \( 55 \) is the hourly rate (cost per hour),
- \( h \) represents the number of hours worked by the electrician.

Answer 6

Part C:

To solve the equation \( 252.50 = 60 + 55h \) using inverse operations, we will isolate the variable \( h \). Here are the steps:

1. **Subtract 60 from both sides** of the equation to eliminate the one-time fee:

\[
252.50 - 60 = 55h
\]

Simplifying the left side:

\[
192.50 = 55h
\]

2. **Divide both sides by 55** to solve for \( h \):

\[
h = \frac{192.50}{55}
\]

Now, performing the division:

\[
h = 3.5
\]

So, the solution is:

\[
h = 3.5
\]

This means it took the electrician **3.5 hours** to complete the repair.

Answer 7

Part D:

The electrician worked for **3.5 hours**, starting at **10:30 a.m.** To determine what time he finished, we can break it down into two parts: 3 hours and 30 minutes.

1. **Adding 3 hours to 10:30 a.m.**:

\[
10:30 \, \text{a.m.} + 3 \, \text{hours} = 1:30 \, \text{p.m.}
\]

2. **Adding 30 minutes to 1:30 p.m.**:

\[
1:30 \, \text{p.m.} + 30 \, \text{minutes} = 2:00 \, \text{p.m.}
\]

So, the electrician finished with the repair at **2:00 p.m.**