Final answer:
Emilia should leave home at 9:45 pm the next day.
Step-by-step explanation:
To determine the latest time Emilia should leave home, we need to calculate the total travel time and add it to the time she wants to arrive at the theater. First, we convert 112 hours to minutes by multiplying by 60: 112 hours * 60 minutes/hour = 6720 minutes. Next, we convert 20 minutes to hours by dividing by 60: 20 minutes / 60 minutes/hour = 1/3 hour. Now, we add the travel time and arrival buffer time to the start time: 7:45 pm + 6720 minutes + 1/3 hour = 7:45 pm + 6720 minutes + 20 minutes = 11140 minutes + 20 minutes = 11160 minutes. Finally, we convert the minutes back to hours and minutes: 11160 minutes / 60 minutes/hour = 186 hours, with 0 minutes remaining. Therefore, Emilia should leave home at 186 hours after 7:45 pm, which is 9:45 pm the next day.