Final answer:
Hannah runs for 1/6 hour in class and 5/8 hour at home. By converting both to a common denominator of 24, adding them, and then converting the result to minutes, she runs for about 47.5 minutes in total.
Step-by-step explanation:
To calculate the total amount of time Hannah runs, we need to add the time she runs in class to the time she runs at home. She runs for 1/6 hour in class and 5/8 hour at home. To add these fractions, it is necessary to have a common denominator.
First, find the least common multiple (LCM) of the denominators 6 and 8, which is 24. Then, convert both fractions to have this common denominator:
- For 1/6, multiply both the numerator and the denominator by 4 to get 4/24.
- For 5/8, multiply both the numerator and the denominator by 3 to get 15/24.
Now that both fractions have a common denominator, you can add them:
4/24 + 15/24 = 19/24
The sum of 19/24 represents the total time Hannah runs. To give an estimate or to express this time in minutes, you can do the following:
(19/24) × 60 minutes = 47.5 minutes
Therefore, Hannah runs for about 47.5 minutes in total.