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.
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Let \( t \) be the travel fee and \( r \) be the hourly rate.
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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: \[ y = t + 6r = 260 \quad \text{(2)} \]
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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): \[ t + 6r = 260 \quad \text{(2)} \]
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We can subtract equation (1) from equation (2): \[ (t + 6r) - (t + 2r) = 260 - 100 \] \[ 4r = 160 \] \[ r = 40 \]
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Now, substitute \( r = 40 \) back into equation (1) to find \( t \): \[ t + 2(40) = 100 \] \[ t + 80 = 100 \] \[ t = 20 \]
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Now we have:
- Travel fee \( t = 20 \)
- Hourly rate \( r = 40 \)
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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: \[ y = 20 + 40x \]