To determine the fraction of time Gerald is in class on Thursday, we need to evaluate his class schedule for that day and compare the scheduled class time to the total available time slots.
Firstly, let's calculate the total minutes available from 8:00 A.M. to 2:15 P.M. on Thursday:
- The first five time slots are each 50 minutes long.
- The sixth time slot is 75 minutes long.
So, the total time is calculated as follows:
[tex]\[ 5 \text{ slots} \times 50 \text{ minutes/slot} + 1 \text{ slot} \times 75 \text{ minutes/slot} \][/tex]
[tex]\[ = 250 \text{ minutes} + 75 \text{ minutes} \][/tex]
[tex]\[ = 325 \text{ minutes} \][/tex]
Thus, there are 325 minutes available on Thursday.
Next, let's identify how many minutes Gerald is actually in class on Thursday:
- Gerald has Math 220 from 9:00 to 9:50 A.M. which is 50 minutes.
- Gerald has English 230 from 10:00 to 10:50 A.M., which is another 50 minutes.
So, the total time Gerald is in class is calculated as follows:
[tex]\[ 50 \text{ minutes} (\text{Math 220}) + 50 \text{ minutes} (\text{English 230}) \][/tex]
[tex]\[ = 100 \text{ minutes} \][/tex]
Therefore, Gerald is in class for 100 minutes on Thursday.
Finally, we need to determine the fraction of time Gerald spends in class out of the total available time. This can be found by dividing the minutes in class by the total available minutes:
[tex]\[ \text{Fraction of time in class} = \frac{\text{Minutes in class}}{\text{Total minutes available}} \][/tex]
[tex]\[ = \frac{100 \text{ minutes}}{325 \text{ minutes}} \][/tex]
To express this fraction as a percentage, we multiply it by 100:
[tex]\[ \frac{100}{325} \times 100 \approx 30.77\% \][/tex]
So, Gerald is scheduled to be in class for approximately 30.77% of the time from 8:00 A.M. to 2:15 P.M. on Thursday.
