Answer: 36 periods in a day
Explanation:
To find the number of periods in a day when each period is reduced to 40 minutes, you can use the ratio of the original period duration to the new period duration.
Original period duration = 45 minutes
New period duration = 40 minutes
The ratio of the original period duration to the new period duration is:
45 minutes / 40 minutes
Now, simplify this ratio:
(45/5) minutes / (40/5) minutes = 9 minutes / 8 minutes
So, each new period is 9/8 times as long as the original period.
Now, to find the number of periods in a day with the new 40-minute duration, you need to divide the total available time in a day by the new period duration:
Total available time in a day = 24 hours * 60 minutes = 1440 minutes
Number of periods with 40-minute duration = Total available time / New period duration
Number of periods = 1440 minutes / 40 minutes = 36 periods
So, when each period is reduced to 40 minutes, there will be a total of 36 periods in a day.