Answer :
To find out how many hours per week Hector exercises and how his rate compares to the fitness challenge rate, let's go through this step by step:
1. Calculate Hector's weekly exercise rate:
- Hector exercises for [tex]\( 11 \frac{1}{2} \)[/tex] hours over a 4-week period.
- First, convert [tex]\( 11 \frac{1}{2} \)[/tex] to an improper fraction: [tex]\(\frac{23}{2}\)[/tex].
- To find the weekly rate, divide the total hours by 4: [tex]\(\frac{23}{2} \div 4 = \frac{23}{8} = 2 \frac{7}{8}\)[/tex].
So, Hector exercises [tex]\( 2 \frac{7}{8} \)[/tex] hours per week.
2. Compare Hector's rate to the fitness challenge rate:
- The fitness challenge requires students to exercise at least [tex]\( 2 \frac{1}{2} \)[/tex] hours per week.
- Compare [tex]\( 2 \frac{7}{8} \)[/tex] to [tex]\( 2 \frac{1}{2} \)[/tex].
Since [tex]\( 2 \frac{7}{8} \)[/tex] is greater than [tex]\( 2 \frac{1}{2} \)[/tex], we conclude:
Because [tex]\( 2 \frac{7}{8} \)[/tex] is greater than [tex]\( 2 \frac{1}{2} \)[/tex], Hector's rate is greater than the fitness challenge rate.
Therefore, Hector exceeds the exercise requirement set by the fitness challenge!
1. Calculate Hector's weekly exercise rate:
- Hector exercises for [tex]\( 11 \frac{1}{2} \)[/tex] hours over a 4-week period.
- First, convert [tex]\( 11 \frac{1}{2} \)[/tex] to an improper fraction: [tex]\(\frac{23}{2}\)[/tex].
- To find the weekly rate, divide the total hours by 4: [tex]\(\frac{23}{2} \div 4 = \frac{23}{8} = 2 \frac{7}{8}\)[/tex].
So, Hector exercises [tex]\( 2 \frac{7}{8} \)[/tex] hours per week.
2. Compare Hector's rate to the fitness challenge rate:
- The fitness challenge requires students to exercise at least [tex]\( 2 \frac{1}{2} \)[/tex] hours per week.
- Compare [tex]\( 2 \frac{7}{8} \)[/tex] to [tex]\( 2 \frac{1}{2} \)[/tex].
Since [tex]\( 2 \frac{7}{8} \)[/tex] is greater than [tex]\( 2 \frac{1}{2} \)[/tex], we conclude:
Because [tex]\( 2 \frac{7}{8} \)[/tex] is greater than [tex]\( 2 \frac{1}{2} \)[/tex], Hector's rate is greater than the fitness challenge rate.
Therefore, Hector exceeds the exercise requirement set by the fitness challenge!