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 find an equation that represents the total cost of a repair \( y \) as a function of the number of hours spent fixing a leak \( x \), we can analyze the given information and calculate the travel fee and the hourly rate.

1. Let \( t \) be the travel fee and \( r \) be the hourly rate.

2. From the problem, we have two scenarios:
- For a repair that takes 2 hours, the total cost is $100:
\[
y = t + 2r = 100 \quad \text{(1)}
\]
- For a repair that takes 6 hours, the total cost is $260:
\[
y = t + 6r = 260 \quad \text{(2)}
\]

3. We can solve these two equations to find the values of \( t \) and \( r \).

- From equation (1):
\[
t + 2r = 100 \quad \text{(1)}
\]
- From equation (2):
\[
t + 6r = 260 \quad \text{(2)}
\]

4. We can subtract equation (1) from equation (2):
\[
(t + 6r) - (t + 2r) = 260 - 100
\]
\[
4r = 160
\]
\[
r = 40
\]

5. Now, substitute \( r = 40 \) back into equation (1) to find \( t \):
\[
t + 2(40) = 100
\]
\[
t + 80 = 100
\]
\[
t = 20
\]

6. Now we have:
- Travel fee \( t = 20 \)
- Hourly rate \( r = 40 \)

7. The total cost of a repair as a function of the number of hours \( x \) can be expressed as:
\[
y = t + rx
\]
Substituting the values of \( t \) and \( r \):
\[
y = 20 + 40x
\]

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