Question

a repair person charges a travel fee to visit a home and an hourly fee for the time spent fixing a leak. a repair that takes 2hours cost $100 a repair that takes 6hours cost $260

write an equation to represent the total cost of a repair,y, as a function of the number of hours spent fixing a leak, x.

Answer 1

To write an equation representing the total cost \( y \) as a function of the number of hours spent fixing a leak \( x \), we need to determine the fixed travel fee and the hourly cost based on the information provided.

1. **Identify the total cost for each scenario:**

- For 2 hours, the total cost is $100:
\[
y = \text{Travel fee} + (\text{Hourly fee}) \times 2
\]
\[
100 = \text{Travel fee} + 2h
\]

- For 6 hours, the total cost is $260:
\[
y = \text{Travel fee} + (\text{Hourly fee}) \times 6
\]
\[
260 = \text{Travel fee} + 6h
\]

2. **Set up the equations using \( t \) for the travel fee and \( h \) for the hourly fee:**

From the first equation:
\[
100 = t + 2h \quad \text{(1)}
\]

From the second equation:
\[
260 = t + 6h \quad \text{(2)}
\]

3. **Solve the system of equations:**

Subtract equation (1) from equation (2):
\[
260 - 100 = (t + 6h) - (t + 2h)
\]
\[
160 = 4h
\]
\[
h = 40
\]

Now substitute \( h = 40 \) back into equation (1):
\[
100 = t + 2(40)
\]
\[
100 = t + 80
\]
\[
t = 20
\]

4. **Formulate the total cost equation:**

Now that we have the values for \( t \) and \( h \):
- Travel fee \( t = 20 \)
- Hourly fee \( h = 40 \)

The total cost equation \( y \) in terms of hours \( x \) is:
\[
y = 20 + 40x
\]

So, the final equation representing the total cost of a repair as a function of the number of hours spent fixing a leak is:
\[
y = 20 + 40x
\]