To compare the hours Maddie spends in a cast and the total hours for the week, we need to establish a clear understanding of the proportional relationship between the hours of sleep and the hours in the cast.
Given:
- Hours in cast per day: 18 hours
- Total days in a week: 7 days
- Total hours in a week: 91 hours
Steps to Analyze:
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Calculate Total Time Spent in Cast in a Week:
- Hours in cast per week = 18 hours/day × 7 days = 126 hours.
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Compare to Weekly Hours:
- Total hours in a week = 24 hours/day × 7 days = 168 hours.
- Therefore, time spent not in the cast = Total weekly hours - Total hours in cast
- Time spent not in cast in a week = 168 hours - 126 hours = 42 hours.
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Analyze Proportional Relationship:
- This means that out of the total 168 hours in a week, 126 hours are spent in the cast and 42 hours are left over (which might include sleep and other activities).
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Sleep Hours:
- If we consider the total number of hours left after the cast (42 hours), we can think about how many of those hours are actually spent sleeping. If Maddie sleeps in a proportional relationship to the time spent in the cast, she may not be sleeping full 8 hours per night (56 hours total in a week).
To summarize:
- Maddie is in a cast for 126 hours of the week out of a total of 168 hours.
- Thus, she spends a significant amount of time in the cast, leading to only 42 hours available for other activities such as sleep, meals, and other daily routines.
Proportional Relationship Conclusion:
Maddie's hours in the cast (126 hours) are proportional to her total available hours in the week (168 hours), and her remaining hours (42) reflect the constrained time for other activities due to the duration spent in the cast.
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