High School

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.

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!