The Correct Answer and Explanation is:
Of course. Based on the image provided, here is the correct answer and a detailed explanation.
Correct Answer
Hector exercises for 2 and 7/8 hours per week.
To compare Hector’s rate to the fitness challenge rate, one would need the specific value for the challenge rate, which is not visible in the image. However, the process involves comparing the two numbers to determine if Hector’s rate is greater than, less than, or equal to the challenge rate.
Explanation
The first question asks for the total number of hours Hector exercises per week. The image shows this value is 2 and 7/8 hours. This is a mixed number, which combines a whole number (2) and a proper fraction (7/8). It means Hector exercises for two full hours plus an additional 7/8 of an hour. To better understand this duration, we can convert the fractional part into minutes. Since there are 60 minutes in an hour, we calculate 7/8 of 60 minutes:
(7 / 8) * 60 = 420 / 8 = 52.5 minutes.
So, Hector exercises for a total of 2 hours and 52.5 minutes each week.
The second question requires a comparison between Hector’s exercise rate (2 7/8 hours) and a “fitness challenge rate.” Since the challenge rate is missing, we can explain the comparison process with a hypothetical example. Let’s assume the fitness challenge rate was 2 and 1/2 hours per week.
To compare 2 7/8 and 2 1/2, we first look at the whole numbers. Both are 2, so we must then compare the fractions: 7/8 and 1/2. To compare fractions, it is easiest to find a common denominator. The least common denominator for 8 and 2 is 8.
We convert 1/2 into eighths: 1/2 is equal to 4/8.
Now we can compare the two rates:
Hector’s Rate: 2 7/8
Challenge Rate: 2 4/8
Since 7 is greater than 4, the fraction 7/8 is greater than 4/8. Therefore, Hector’s rate of 2 7/8 hours is greater than the hypothetical challenge rate of 2 1/2 hours. The final comparison would be written as: 2 7/8 > 2 1/2.
