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Measurement - Timelines, Calendars, 24-Hour Time, and Timetables

Grade 6IB

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

🔑Concepts

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The 24-hour clock system uses four digits to represent time, from 00:0000:00 (midnight) to 23:5923:59. To convert 1212-hour PM times to 2424-hour time, add 1212 to the hours (e.g., 4:00 PM4:00\text{ PM} becomes 16:0016:00 hours).

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A leap year occurs every 44 years and contains 366366 days instead of the usual 365365 days. The extra day is added to February (2929 days).

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Time intervals or durations are calculated by finding the difference between the 'End Time' and 'Start Time'. If the minutes in the start time are greater than the minutes in the end time, regroup 11 hour as 6060 minutes.

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Timetables are organized lists of information (like bus or train schedules) used to determine departure times, arrival times, and total journey durations.

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A timeline is a visual representation of events in chronological order, helping to calculate the time elapsed between significant dates or historical periods.

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The number of days in months varies: September, April, June, and November have 3030 days; February has 2828 (or 2929); all others have 3131 days.

📐Formulae

1 hour=60 minutes1\text{ hour} = 60\text{ minutes}

1 minute=60 seconds1\text{ minute} = 60\text{ seconds}

Duration=End Time−Start Time\text{Duration} = \text{End Time} - \text{Start Time}

24-hour time (PM)=12-hour time+12 hours24\text{-hour time (PM)} = 12\text{-hour time} + 12\text{ hours}

1 common year=52 weeks+1 day1\text{ common year} = 52\text{ weeks} + 1\text{ day}

💡Examples

Problem 1:

Convert 8:25 PM8:25\text{ PM} into 2424-hour time format.

Solution:

8:25 PM→8+12=20→20:258:25\text{ PM} \rightarrow 8 + 12 = 20 \rightarrow 20:25

Explanation:

To convert PM time to 24-hour time, we add 1212 to the hour portion and write it as a four-digit number without the PM suffix.

Problem 2:

A flight departs at 22:4522:45 on Monday and arrives at 03:1503:15 on Tuesday. Calculate the total duration of the flight.

Solution:

22:45 to 00:00=1 hour 15 minutes22:45 \text{ to } 00:00 = 1\text{ hour } 15\text{ minutes} 00:00 to 03:15=3 hours 15 minutes00:00 \text{ to } 03:15 = 3\text{ hours } 15\text{ minutes} Total=1h 15m+3h 15m=4 hours 30 minutes\text{Total} = 1\text{h } 15\text{m} + 3\text{h } 15\text{m} = 4\text{ hours } 30\text{ minutes}

Explanation:

First, calculate the time until midnight (24:0024:00), then add the time from midnight to the arrival time. 24:00−22:45=1 hour 15 minutes24:00 - 22:45 = 1\text{ hour } 15\text{ minutes}. Then 1:15+3:15=4:301:15 + 3:15 = 4:30.

Problem 3:

Calculate the duration between 09:5009:50 and 14:2014:20 using vertical subtraction.

Solution:

We need to subtract 09:5009:50 from 14:2014:20. Since 20<5020 < 50, we borrow 11 hour (6060 minutes) from 1414 hours, making it 1313 hours and 8080 minutes (20+6020 + 60): 13:80−09:5004:30\begin{array}{r} 13:80 \\ - 09:50 \\ \hline 04:30 \end{array} The duration is 44 hours and 3030 minutes.

Explanation:

When the minutes being subtracted are larger than the minutes available, regroup 11 hour into 6060 minutes to perform the subtraction.

Problem 4:

If a project starts on 25th February 2024 and lasts for 1010 days, what is the completion date?

Solution:

2024 is a leap year, so February has 2929 days. Days remaining in Feb: 29−25=429 - 25 = 4 days. Days left for March: 10−4=610 - 4 = 6 days. Completion date: 6th March.

Explanation:

Identify if it is a leap year first. Since 2024 is divisible by 44, February has 2929 days. Count the remaining days in the current month and carry over the rest to the next month.