time duration

We will learn

• Representation of time in 12 and 24-hour clocks.
• How to calculate time duration.

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12-hour and 24-hour Clock

There are two ways to represent time.

• The 12 hours clock breaks the 24 hours of a day into two portions, 12 hrs from midnight to midday and then 12 hours from midday to midnight. 00:00 or 12 o'clock midnight till 11:59 in the morning is midnight to noon time, in English, we express this time in AM, and 12 o'clock noon till 11:59 at night is noon to midnight time, in English, we express this time in PM.
• 24 hours clock does not break the day into day and night but calculates time starting at midnight. The time is shown as how many hours and minutes since midnight. The hours start at zero and go through to 23. So 00:00 to 11:59 is midnight to noon time and 12:00 to 23:59 is noon to midnight time.

The below figure shows the representation of time in the 12-Hour and 24-Hour format.

Rules for converting 12 hours time to 24 hours time:

• If the hour is 12 noon then in the 24-hour clock it is 12:00.
• If the hour is 12 midnight, then in the 24-hour clock it is 00.
• If the hour is after 12 noon, then add 12 to the hour. For example, 1 PM is 12 + 1, that is 13:00 in 24-hour clock
• If the hour is before 12 noon, it stays the same and does not change. 11 AM is represented as 11:00 in the 24-hour clock.
• If the hour is less than 10, then add a zero before the digit, for example, 9 AM is 09:00.

Example:
1:30 in the morning - 01:30
12:45 in the afternoon - 12:45
11:32 in the morning  - 11:32
4:20 in the afternoon - 16:20 (Add 12 to 4, 12 + 4 = 16)

Rules for converting 24 hours time to 12 hours time:

• Starting from the first hour of the day (00:00 or midnight to 00:59), add 12 hours and AM to the time. For example, 00:30 is 12:30 AM in the 12-hour clock
• From 1:00 to 11:59, simply add AM to the time. For example, 09:00 is 9 AM in the 12-hour clock.
• For times between 13:00 to 23:59, subtract 12 hours and add PM to the time. For example, 16:40 is 4:40 PM in the 12-hour clock.

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Calculating Time Duration

To determine the number of hours and minutes between two chosen times within the same day, convert the time into a 24-hour clock and then subtract. Let us understand this with an example.

Example 1: Find the time interval between 9 AM and 3 PM
Start time : 09:00 (morning) is 09:00 (24-hour clock)
End time : 03:00 (Afternoon) is 3 +12 = 15:00 (24-hour clock)

End time - Start time = 15:00 − 09:00 = 06:00 = 6 hours

Example 2: Find the time interval between Morning 9:40  and Afternoon 3:10.
Start time : 09:40 AM is 09:40 ( 24-hour clock)
End time : 03:10 PM is 15:10 (24-hour clock)
Check the minutes, the start time has a larger value for minutes than the end time, in such case you need to treat the hour and minute portion separately. Add 60 to the number of minutes in the ending time, and subtract 1 hour from the hour portion of the ending time. Here ending time will be
Hours: 15 − 1 = 14
Minutes: 10 + 60 = 70 
Now subtract 14:70 − 09:40 = 05:30 = 5 hours 30 minutes is the time difference

Example 3: What will be the time after 40 minutes, if it is 2:45 in the afternoon now?
Converting time to 24 hour clock, 2:45PM = 14:45
Add 40 min + 14:45 = 14 hours 85 min
break 85 min in hours and minutes = 60 min + 25 min = 1 hour  + 25 min
Add 1 hour to 14 hours = 15 hours
Time after 40 minutes will be 15 hours 25 min or 3:25 in the afternoon.

Example 4: What was the time before 50 minutes if the current time is 11:00 in the morning?
Subtract 50 minutes from 11:00(24-hour clock time)
As the 50 value is bigger than the minute value 00, therefore deduct 1 hour from 11 and add 60 to the minute part.
So 11:00 can also be written as 10:60.
10:60 − 50 min = 10:10
The time before 50 minutes was 10:10 in the morning.

Example 5: I studied Mathematics for 2 hours 20 minutes and Social Studies for 1 hour 30 minutes, what is the total time spent in studies?
Add Mathematics and Social Studies time.
   2 hours 20 minutes
+1 hour 30 minutes
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   3 hours 50 minutes
Note: If the minute total is more than 60 then add 1 hour to the hour value and subtract 60 minutes from the minutes' value.