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.

y = __x + __

Answer 1

To create an equation that represents the total cost of a repair, we need to identify the travel fee (the fixed cost) and the hourly fee (the variable cost).

Given the information:

1. If the repair takes 2 hours, the total cost is $100.
2. If the repair takes 6 hours, the total cost is $260.

We can set up a system of equations to solve for the hourly fee and the travel fee.

Let:
- \( b \) be the travel fee (fixed cost),
- \( p \) be the hourly fee.

From the given information, we can set up the following equations:

1. \( 2p + b = 100 \) (for 2 hours)
2. \( 6p + b = 260 \) (for 6 hours)

Now, let's subtract the first equation from the second:

\[
(6p + b) - (2p + b) = 260 - 100
\]

This simplifies to:

\[
4p = 160
\]

Dividing both sides by 4, we find:

\[
p = 40
\]

Now that we have the hourly fee, we can substitute \( p \) back into one of the original equations to find \( b \):

Using \( 2p + b = 100 \):

\[
2(40) + b = 100
\]
\[
80 + b = 100
\]
\[
b = 20
\]

Now we have the values for both the travel fee and the hourly fee:

- Travel fee (\( b \)) = $20
- Hourly fee (\( p \)) = $40

Therefore, the equation representing the total cost of a repair \( y \) as a function of the number of hours spent fixing a leak \( x \) is:

\[
y = 40x + 20
\]

So in the format \( y = \_\_x + \_\_ \):

\[
y = 40x + 20
\]