Final answer:
The two plumbers will cost the same after 3 hours of work, with a total cost of $245. This result does not match any of the answer choices provided in the question, suggesting there may be an error in the question or options given.
Step-by-step explanation:
To find out at how many hours plumbing company A and plumber B will cost the same, we need to set up an equation where the costs from both are equal. Let's denote h as the number of hours of plumbing work.
For company A: Cost = $55/h * h + $80 (service call)
For plumber B: Cost = $60/h * h + $65 (service call)
Setting the two equations equal to each other gives us:
55h + 80 = 60h + 65
Now, we solve for h by subtracting 55h from both sides:
80 = 5h + 65
Then, subtract 65 from both sides:
15 = 5h
And finally, divide both sides by 5:
3 = h
The two plumbers will cost the same after 3 hours of work.
To find the cost at that point, we can substitute h = 3 into either company's cost equation. Using company A's equation:
Cost = 55 * 3 + 80
Cost = 165 + 80
Cost = $245
So, after 3 hours, both plumbing services will cost $245, which is not one of the listed options, indicating a potential mistake in the question or the answer choices given.