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.

How many hours per week does Hector exercise?

? hour(s) per week

Sure, let's solve the problem step-by-step.

Hector's school encourages students to exercise at least [tex]$2 \frac{1}{2}$[/tex] hours per week. Hector wants to know how his exercise rate compares.

First, let's see how many hours Hector exercises in total over the 4-week period:
- Hector exercises [tex]$ 11 \frac{1}{2} $[/tex] hours in 4 weeks.

Now, let's find out how many hours Hector exercises per week. To do this, we divide the total hours by the number of weeks:
- Total hours exercised = [tex]$ 11 \frac{1}{2} $[/tex] hours
- Number of weeks = 4

Convert [tex]$ 11 \frac{1}{2} $[/tex] to a decimal:
[tex]\[ 11 \frac{1}{2} = 11 + 0.5 = 11.5 \][/tex] hours

Now, we divide the total hours by the number of weeks to find the average hours per week:
[tex]\[ \text{Average hours per week} = \frac{11.5 \text{ hours}}{4 \text{ weeks}} \][/tex]

Perform the division:
[tex]\[ \frac{11.5}{4} = 2.875 \][/tex]

So, Hector exercises [tex]$ 2.875 $[/tex] hours per week.

Therefore, Hector exercises approximately [tex]$ 2.875 $[/tex] hours per week.