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:
- If the repair takes 2 hours, the total cost is $100.
- 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:
- \( 2p + b = 100 \) (for 2 hours)
- \( 6p + b = 260 \) (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 \( y = __x + __ \):
\[ y = 40x + 20 \]