Final answer:
To determine when Paul's Plumbing is the same price or cheaper than Perfect Plumbing, we equate their cost equations and find that they charge the same amount at 40 hours. Paul's Plumbing will be the same price or cheaper for any number of hours up to and including 40 hours.
Step-by-step explanation:
To find out at how many hours Paul's Plumbing charges a $40 house call fee and $4 per hour will be the same price or cheaper than Perfect Plumbing, which charges no fee and $5 per hour, we can set up an equation. For Paul's Plumbing, the cost (C) can be represented as C = 40 + 4h, where h is the number of hours. For Perfect Plumbing, the cost (C) is given by C = 5h. To determine the point where both companies charge the same amount, we'll set the costs equal to each other and solve for h:
40 + 4h = 5h
Subtracting 4h from both sides of the equation, we get:
40 = h, which means that at 40 hours, both companies will charge the same total cost. To find when Paul's Plumbing is cheaper, we can compare costs for a number of hours less than 40. We can see that for any value of h less than 40, the total cost for Paul's Plumbing will still be less than Perfect Plumbing. Therefore, Paul's Plumbing will be same price or cheaper for any number of hours up to and including 40 hours.