Final answer:
The costs of two plumbers will be the same after 7.5 hours of work. To find this, we solve for the time 'h' when the cost equations of the plumbers, C1 = 20h + 15 and C2 = 18h + 30, are equal.
Step-by-step explanation:
To determine after how many hours the cost of two different plumbers will be the same, we need to find the point where the two cost equations intersect. The first plumber charges $20 an hour plus a $15 flat fee, so their cost equation is C1 = 20h + 15, where C1 represents the total cost for the first plumber and h represents the number of hours worked.
The second plumber charges $18 an hour plus a $30 flat fee, resulting in a cost equation of C2 = 18h + 30. The costs will be the same when C1 = C2, thus we set the equations equal to each other and solve for h:
20h + 15 = 18h + 30
- Subtract 18h from both sides: 2h + 15 = 30
- Subtract 15 from both sides: 2h = 15
- Divide by 2: h = 7.5
Hence, after 7.5 hours, the cost of hiring either plumber will be the same.