Answer :
To solve the problem and find out how many hours per week Hector exercises and compare it to the fitness challenge rate, follow these steps:
1. Total Hours Hector Exercises Over 4 Weeks:
- Hector exercises for [tex]\(11 \frac{1}{2}\)[/tex] hours over 4 weeks. This can be converted to a decimal:
[tex]\[
11 \frac{1}{2} = 11 + 0.5 = 11.5 \text{ hours}
\][/tex]
2. Calculate Hector's Weekly Exercise Rate:
- To find out how many hours per week Hector exercises, divide the total exercise hours by the number of weeks:
[tex]\[
\text{Weekly Exercise Rate} = \frac{11.5}{4} = 2.875 \text{ hours per week}
\][/tex]
- So, Hector exercises 2.875 hours per week.
3. Fitness Challenge Weekly Exercise Rate:
- The fitness challenge encourages at least [tex]\(2 \frac{1}{2}\)[/tex] hours per week. Converting this to a decimal gives:
[tex]\[
2 \frac{1}{2} = 2 + 0.5 = 2.5 \text{ hours per week}
\][/tex]
4. Compare Hector's Rate to the Fitness Challenge Rate:
- Now, compare Hector's weekly rate to the challenge rate:
- Hector's rate ([tex]\(2.875\)[/tex] hours per week) is greater than the challenge rate ([tex]\(2.5\)[/tex] hours per week).
5. Conclusion:
- Because [tex]\(2.875 \, \text{hours}\)[/tex] is greater than [tex]\(2.5 \, \text{hours}\)[/tex], Hector's rate is greater than the fitness challenge rate.
In summary, Hector exercises [tex]\(2.875\)[/tex] hours per week, which is greater than the required [tex]\(2.5\)[/tex] hours per week for the fitness challenge.
1. Total Hours Hector Exercises Over 4 Weeks:
- Hector exercises for [tex]\(11 \frac{1}{2}\)[/tex] hours over 4 weeks. This can be converted to a decimal:
[tex]\[
11 \frac{1}{2} = 11 + 0.5 = 11.5 \text{ hours}
\][/tex]
2. Calculate Hector's Weekly Exercise Rate:
- To find out how many hours per week Hector exercises, divide the total exercise hours by the number of weeks:
[tex]\[
\text{Weekly Exercise Rate} = \frac{11.5}{4} = 2.875 \text{ hours per week}
\][/tex]
- So, Hector exercises 2.875 hours per week.
3. Fitness Challenge Weekly Exercise Rate:
- The fitness challenge encourages at least [tex]\(2 \frac{1}{2}\)[/tex] hours per week. Converting this to a decimal gives:
[tex]\[
2 \frac{1}{2} = 2 + 0.5 = 2.5 \text{ hours per week}
\][/tex]
4. Compare Hector's Rate to the Fitness Challenge Rate:
- Now, compare Hector's weekly rate to the challenge rate:
- Hector's rate ([tex]\(2.875\)[/tex] hours per week) is greater than the challenge rate ([tex]\(2.5\)[/tex] hours per week).
5. Conclusion:
- Because [tex]\(2.875 \, \text{hours}\)[/tex] is greater than [tex]\(2.5 \, \text{hours}\)[/tex], Hector's rate is greater than the fitness challenge rate.
In summary, Hector exercises [tex]\(2.875\)[/tex] hours per week, which is greater than the required [tex]\(2.5\)[/tex] hours per week for the fitness challenge.
