Explain how the rate of change for time spent working in ALEKS might change if you watched 3 fewer television shows next week. if each show is 120 hrs long.

To analyze how the rate of change for time spent working in ALEKS might change with the reduction of television watching, we can follow these steps:

1. Break Down the Problem

• Determine the total time saved by watching 3 fewer television shows.
• Assess how this saved time can affect time spent working in ALEKS.

2. Relevant Concepts

• Each television show is 120 hours long.
• The total time spent on television shows is calculated as: $\text{Total Time Saved} = \text{Number of Shows} \times \text{Hours per Show}$

3. Analysis and Detail

• Calculate the total hours saved for 3 fewer shows: $\text{Total Time Saved} = 3 \times 120 \, \text{hours} = 360 \, \text{hours}$
• This saved time could be reallocated to ALEKS, potentially increasing the total time spent there.

4. Verify and Summarize

• The calculation shows that by watching 3 fewer shows, you save 360 hours weekly.
• This extra 360 hours can now be considered as additional time that could be spent on ALEKS.

Final Answer

If you watch 3 fewer television shows next week, you save a total of 360 hours, which can potentially be added to the time spent working in ALEKS.