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Measurement - Elapsed Time and 24-hour Clock

Grade 5IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The 12-hour clock system divides a full day into two 1212-hour periods: a.m. (ante meridiem, before midday) and p.m. (post meridiem, after midday). Visualize a circular clock face numbered 11 to 1212; the hour hand must complete two full circles to represent one whole day of 2424 hours.

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The 24-hour clock measures time continuously from 00:0000:00 (midnight) to 23:5923:59. It does not use a.m. or p.m. labels. Imagine a long horizontal timeline starting at 00:0000:00 at the beginning of the day and stretching to the right until it reaches the next day.

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To convert a 12-hour p.m. time to 24-hour format, add 1212 to the hours (except for 1212 p.m., which stays 12:0012:00). For example, 4:004:00 p.m. becomes 4+12=16:004 + 12 = 16:00. If converting an a.m. time, the hours remain the same (except for 1212 a.m., which becomes 00:0000:00).

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To convert a 24-hour time to 12-hour format, look at the hours. If the hour is 0000, it becomes 1212 a.m. If the hour is 0101 to 1111, it is a.m. If the hour is 1212, it is 1212 p.m. If the hour is 1313 to 2323, subtract 1212 and add p.m.

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Elapsed time is the 'length' or duration of time that passes between a start time and an end time. This can be visualized using a 'Time Mountain' diagram where you draw large peaks for 11-hour jumps and small hills for 55-minute or 11-minute jumps to count forward from the start.

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Calculating elapsed time often requires regrouping based on 6060 because there are 6060 minutes in an hour. When subtracting, if the minutes in the end time are fewer than the minutes in the start time, you must borrow 11 hour (6060 minutes) from the hours column.

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Midnight is the transition point between days, represented as 00:0000:00 on the 24-hour clock. Noon is the middle of the day, represented as 12:0012:00. On a timeline, midnight is the starting point of a 2424-hour cycle.

📐Formulae

1texthour=60textminutes1 \\text{ hour} = 60 \\text{ minutes}

1textminute=60textseconds1 \\text{ minute} = 60 \\text{ seconds}

text24−hourHour=text12−hourHour(p.m.)+12\\text{24-hour Hour} = \\text{12-hour Hour (p.m.)} + 12

textElapsedTime=textEndTime−textStartTime\\text{Elapsed Time} = \\text{End Time} - \\text{Start Time}

textTotalMinutes=(textHourstimes60)+textRemainingMinutes\\text{Total Minutes} = (\\text{Hours} \\times 60) + \\text{Remaining Minutes}

💡Examples

Problem 1:

A flight departs at 10:4510:45 a.m. and lands at 3:203:20 p.m. How long was the flight?

Solution:

Step 1: Convert both times to 24-hour format. 10:4510:45 a.m. is 10:4510:45. 3:203:20 p.m. is 3+12=15:203 + 12 = 15:20. \nStep 2: Set up the subtraction: 15:20−10:4515:20 - 10:45. \nStep 3: Since 2020 minutes is less than 4545 minutes, borrow 11 hour from 1515 hours. 15:2015:20 becomes 14:8014:80 (60+20=8060 + 20 = 80). \nStep 4: Subtract the hours: 14−10=414 - 10 = 4 hours. \nStep 5: Subtract the minutes: 80−45=3580 - 45 = 35 minutes. \nTotal duration: 44 hours and 3535 minutes.

Explanation:

Converting to 24-hour time makes it easier to subtract across the noon boundary. We use regrouping because 11 hour equals 6060 minutes.

Problem 2:

Convert the 24-hour time 21:1521:15 to 12-hour format.

Solution:

Step 1: Check if the hour is greater than 1212. Here, 21>1221 > 12. \nStep 2: Subtract 1212 from the hours: 21−12=921 - 12 = 9. \nStep 3: Since the original hour was greater than 1212, the time is p.m. \nFinal answer: 9:159:15 p.m.

Explanation:

In the 24-hour system, any hour from 1212 to 2323 represents the afternoon or evening (p.m.). Subtracting 1212 provides the equivalent 12-hour clock value.