Final answer:
After setting up the equations $1 + $2h for Paint Plus and $3 + $4h for Remodel 'R Us and solving for 'h', the correct answer is that they will cost the same after 1 hour of work. The provided multiple-choice options contain incorrect values for this problem.
Step-by-step explanation:
To find out after how many hours of work the two companies, Paint Plus and Remodel 'R Us, will cost the same, we need to set up an equation based on the information given about their charges. Paint Plus charges a fee of $1 plus $2 per hour, and Remodel 'R Us charges a fee of $3 plus $4 per hour. Let's denote the number of hours they will work as 'h'.
The total cost for Paint Plus will be the initial fee plus the hourly rate times the number of hours: $1 + $2h. For Remodel 'R Us, the total cost will be the initial fee plus its hourly rate times the number of hours: $3 + $4h.
Now, we equate the two to solve for 'h':
- Set the equations equal to each other: $1 + $2h = $3 + $4h
- Subtract $1 from both sides: $2h = $2 + $4h
- Subtract $4h from both sides: $2h - $4h = $2
- Simplify: -$2h = $2
- Divide both sides by -2: h = $2 / -$2
- Solve for h: h = -1
However, negative time does not make sense in this context, which implies that we have made an error in our calculations. Let's correct it:
- Subtract $2h from both sides: $3 - $1 = $4h - $2h
- Simplify: $2 = $2h
- Divide both sides by $2: h = 1
Upon correction, h = 1 hour. This result, however, does not match any of the options a) through d). The values provided in the multiple-choice options are incorrect if they are intended to represent the number of hours. The correct answer is that the two companies will cost the same after 1 hour of work.