Final answer:
The total cost for both contractors will be the same after 10 hours of work. This is found by setting up and solving equations that represent the cost for each contractor and finding the point at which these equations intersect.
Step-by-step explanation:
To determine after how many hours the total cost of both contractors will be the same, we need to set up equations for each contractor and find the point where they intersect. For the first contractor with an initial fee of $250 and an hourly rate of $40 per hour, the total cost can be represented by the equation C1 = 250 + 40h, where C1 is the total cost and h is the number of hours worked.
For the second contractor with an initial fee of $150 and an hourly rate of $50 per hour, the equation is C2 = 150 + 50h.
To find out when the costs are equal, we set the equations equal to each other:
250 + 40h = 150 + 50h
Solving for h, we subtract 40h from both sides:
250 = 150 + 10h
Then, we subtract 150 from both sides to solve for h:
100 = 10h
Dividing both sides by 10 gives us:
h = 10
Therefore, after 10 hours, the total cost for both contractors will be the same.