Hector's school is holding a fitness challenge. Students are encouraged to exercise at least [tex]2 \frac{1}{2}[/tex] hours per week. Hector exercises about the same number of hours each week. During a 4-week period, he exercises for [tex]11 \frac{1}{2}[/tex] hours. Hector wants to compare his exercise rate with the fitness challenge rate.

1. How many hours per week does Hector exercise?
- [tex]2 \frac{7}{8}[/tex] hour(s) per week

2. How does Hector's rate compare to the fitness challenge rate?
- Because [tex]2 \frac{7}{8}[/tex] [tex]\square[/tex] [tex]2 \frac{1}{2}[/tex], Hector's rate is [tex]\square[/tex] the fitness challenge rate.

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!