To determine the finishing time of the parents' evening, let's break down the problem step by step.
1. Starting Time: The parents' evening begins at 15:45.
2. Number and Duration of Appointments: There are 20 consecutive appointments, and each appointment lasts for 10 minutes.
3. Total Duration of the Appointments:
- Each appointment is 10 minutes.
- There are 20 appointments.
- Therefore, the total duration for the appointments = [tex]\( 20 \times 10 = 200 \)[/tex] minutes.
4. Break Duration: There is a break of 15 minutes during the evening.
5. Total Duration Including the Break:
- Total duration for appointments = 200 minutes.
- Break duration = 15 minutes.
- Therefore, the total duration including the break = [tex]\( 200 + 15 = 215 \)[/tex] minutes.
6. Calculate the End Time:
- Start at 15:45.
- We need to add 215 minutes to the starting time.
7. Convert Minutes to Hours and Minutes:
- 215 minutes is equivalent to 3 hours and 35 minutes (since [tex]\( 215 \div 60 = 3 \)[/tex] hours and the remainder is 35 minutes).
8. Adding the Total Duration to the Starting Time:
- Start hour: 15
- Start minute: 45
- Adding 3 hours to the start hour: [tex]\( 15 + 3 = 18 \)[/tex]
- Adding 35 minutes to the start minute: [tex]\( 45 + 35 = 80 \)[/tex] minutes.
9. Adjusting if Minutes Exceed 60:
- 80 minutes is 1 hour and 20 minutes (since [tex]\( 80 \div 60 = 1 \)[/tex] hour and the remainder is 20 minutes).
- Adding this hour to the previously calculated hour: [tex]\( 18 + 1 = 19 \)[/tex]
10. Final Calculation:
- So, we add the remaining 20 minutes to 18:00 to get the final finishing time.
Therefore, the parents' evening was due to finish at 19:20 (using the 24-hour clock).
