1. The problem states that the elapsed time from 10:30 am to 12:15 pm is calculated. 2. To find the elapsed time, subtract the start time from the end time: $$12:15 - 10:30$$ 3. Convert times to hours and minutes: - Start time: 10 hours 30 minutes - End time: 12 hours 15 minutes 4. Calculate the difference: - Hours: $12 - 10 = 2$ hours - Minutes: $15 - 30 = -15$ minutes (since minutes are negative, subtract 1 hour and add 60 minutes) 5. Adjusting for negative minutes: - Hours: $2 - 1 = 1$ hour - Minutes: $-15 + 60 = 45$ minutes 6. So, elapsed time is $1$ hour and $45$ minutes. 7. Convert $45$ minutes to hours: $$45 \text{ minutes} = \frac{45}{60} = 0.75 \text{ hours}$$ 8. Total elapsed time in hours: $$1 + 0.75 = 1.75 \text{ hours}$$ 9. Expressing as a fraction: $$1.75 = \frac{7}{4} \text{ hours}$$ 10. If someone ate half an apple per hour, the total apples eaten during the elapsed time is: $$\frac{1}{2} \times \frac{7}{4} = \frac{7}{8} \text{ apples}$$ Therefore, the person ate $\frac{7}{8}$ of an apple during the elapsed time of $1$ hour and $45$ minutes.