Answer :
To determine how Hector's exercise rate compares to the fitness challenge rate, we start by converting the mixed numbers into decimal form.
1. Convert Hector's exercise time to a decimal:
Hector exercises for [tex]\(2 \frac{7}{8}\)[/tex] hours per week. To convert this mixed number to a decimal, do the following:
- The whole number part is 2.
- The fractional part [tex]\(\frac{7}{8}\)[/tex] can be converted to a decimal by dividing 7 by 8, which is 0.875.
Therefore, [tex]\(2 \frac{7}{8}\)[/tex] is equal to [tex]\(2 + 0.875 = 2.875\)[/tex] hours.
2. Convert the fitness challenge rate to a decimal:
The fitness challenge rate is [tex]\(2 \frac{1}{2}\)[/tex] hours per week. To convert this mixed number to a decimal, do the following:
- The whole number part is 2.
- The fractional part [tex]\(\frac{1}{2}\)[/tex] can be converted to a decimal by dividing 1 by 2, which is 0.5.
Therefore, [tex]\(2 \frac{1}{2}\)[/tex] is equal to [tex]\(2 + 0.5 = 2.5\)[/tex] hours.
3. Compare the two rates:
Now that we have the decimal forms, we compare them:
- Hector's rate: 2.875 hours
- Fitness challenge rate: 2.5 hours
Since 2.875 is greater than 2.5, Hector's exercise rate is greater than the fitness challenge rate.
So, Hector's rate is greater than the fitness challenge rate.
1. Convert Hector's exercise time to a decimal:
Hector exercises for [tex]\(2 \frac{7}{8}\)[/tex] hours per week. To convert this mixed number to a decimal, do the following:
- The whole number part is 2.
- The fractional part [tex]\(\frac{7}{8}\)[/tex] can be converted to a decimal by dividing 7 by 8, which is 0.875.
Therefore, [tex]\(2 \frac{7}{8}\)[/tex] is equal to [tex]\(2 + 0.875 = 2.875\)[/tex] hours.
2. Convert the fitness challenge rate to a decimal:
The fitness challenge rate is [tex]\(2 \frac{1}{2}\)[/tex] hours per week. To convert this mixed number to a decimal, do the following:
- The whole number part is 2.
- The fractional part [tex]\(\frac{1}{2}\)[/tex] can be converted to a decimal by dividing 1 by 2, which is 0.5.
Therefore, [tex]\(2 \frac{1}{2}\)[/tex] is equal to [tex]\(2 + 0.5 = 2.5\)[/tex] hours.
3. Compare the two rates:
Now that we have the decimal forms, we compare them:
- Hector's rate: 2.875 hours
- Fitness challenge rate: 2.5 hours
Since 2.875 is greater than 2.5, Hector's exercise rate is greater than the fitness challenge rate.
So, Hector's rate is greater than the fitness challenge rate.
