In this question, we are given the start time and end time of a class, and we also know that four periods of equal duration are held in this interval, with a 5-minute rest after each period.

To find the exact duration of each period, we can subtract the start time from the end time and then subtract the total time taken for the rest periods.

Here`s how we can calculate it:

Start time: 11:00 am

End time: 2:27 pm

Total duration of class: 2 hours and 27 minutes - 11:00 am to 2:27 pm = 3 hours and 27 minutes

Now, let`s calculate the total time taken for the rest periods:

5 minutes rest after each period: 5 minutes x 4 periods = 20 minutes

Subtracting the total time taken for the rest periods from the total duration of class:

3 hours and 27 minutes - 20 minutes = 3 hours and 7 minutes

To find the duration of each period, we divide the total duration of class (3 hours and 7 minutes) by the number of periods (4):

3 hours and 7 minutes / 4 periods = 187 minutes / 4 periods = 46