Final answer:
In 111 hours from 9 o'clock, it will be midnight. This is calculated using modular arithmetic, where 111 modulo 24 equals 15 hours past the nearest whole day, making it 12:00 AM after adding the hours to the starting time of 9 o'clock.
Step-by-step explanation:
Calculating Time in the Future with Modular Arithmetic
If it is currently 9 o'clock and you want to know what time it will be in 111 hours, you can use modular arithmetic to find the answer. Since there are 24 hours in a day, you would calculate 111 modulo 24 to determine how many hours beyond the nearest whole day it will be. The calculation is as follows:
111 hours ÷ 24 hours/day = 4 days and 15 hours.
This means that after 111 hours it will have been 4 full days and an additional 15 hours. Since we started at 9 o'clock, adding 15 hours to 9 o'clock (9 + 15 = 24) brings us to 12 o'clock, or midnight. However, since 24:00 is equivalent to 0:00, the actual time will be 12 o'clock at night or simply 12:00 AM.
Therefore, 111 hours from 9 o'clock will be midnight, precisely 4 days later.