Final answer:
To calculate how long Amanda would take to put up holiday lights alone, we set up an equation based on the rates at which Johnny and Amanda work together and separately. Solving the equation reveals Amanda would take approximately 7.2 hours, which is not listed in the presented options A-D.
Step-by-step explanation:
The question is asking us to find out how long it would take for Amanda to put up the holiday lights by herself, given that when she helped Johnny, the time taken to complete the task was reduced. To solve this problem, we have to set up an equation based on the rates at which Johnny and Amanda work.
Let's define their rates of working as:
- Johnny's rate of work is the entire job done in 4.5 hours, so his rate is 1/4.5 jobs per hour.
- Amanda's rate is unknown, so let's call it 1/A jobs per hour, with A being the number of hours it takes her to finish the job alone.
When Johnny and Amanda work together, their combined rate is 1/4.5 + 1/A, and this equals the rate at which the job is finished when they work together, which is 1/2.88. Setting the equation:
1/4.5 + 1/A = 1/2.88
We find the common denominator and solve for A:
- Multiply through by the common denominator, which is 4.5*A*2.88.
- After the cross multiplying and solving for A, we find that Amanda would take about 7.2 hours to complete the job by herself, which is none of the given options (A-D).
Thus, there seems to be an error in the provided options as they do not match the calculated result.