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Time and Calendar - Duration of Time

Grade 3ICSE

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

🔑Concepts

Duration is the measurement of how long an event lasts. It is the time elapsed between the starting time and the finishing time. Visualize a timeline where the start time is a point on the left and the end time is a point on the right; the length of the line connecting them represents the duration.

The 12-hour clock system uses a.m.\text{a.m.} (Ante Meridiem) for the time from midnight to noon and p.m.\text{p.m.} (Post Meridiem) for the time from noon to midnight. Visualize a circular clock face where the hour hand completes two full circles every day—the first circle for a.m.\text{a.m.} and the second for p.m.\text{p.m.}

To calculate the duration of an event, we find the difference between the end time and the start time. If the minutes in the end time are smaller than the start time, we borrow 1 hour1 \text{ hour} (60 minutes60 \text{ minutes}) from the hour column. Imagine a vertical subtraction table with 'Hours' and 'Minutes' columns.

Time units are hierarchical: 60 seconds60 \text{ seconds} make 1 minute1 \text{ minute}, 60 minutes60 \text{ minutes} make 1 hour1 \text{ hour}, and 24 hours24 \text{ hours} make 1 day1 \text{ day}. Visualize a set of nesting boxes where 6060 tiny 'second' blocks fit into 11 'minute' box, and 6060 'minute' boxes fit into 11 'hour' box.

A calendar helps track days, weeks, and months. There are 7 days7 \text{ days} in a week and 12 months12 \text{ months} in a year. Visualize a grid with 77 columns representing the days of the week (Sunday to Saturday) and several rows representing the weeks in a month.

The number of days in months varies between 2828 and 3131. You can use the 'Knuckle Rule' to remember: knuckles represent months with 31 days31 \text{ days} (January, March, May, July, August, October, December), while the gaps between knuckles represent months with 30 days30 \text{ days} (April, June, September, November), except February.

A leap year occurs every 44 years and has 366 days366 \text{ days} instead of 365365. In a leap year, February has 29 days29 \text{ days} instead of 2828. Imagine a calendar where an extra block is added to the end of February once every four years.

📐Formulae

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

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

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

1 day=24 hours1 \text{ day} = 24 \text{ hours}

1 week=7 days1 \text{ week} = 7 \text{ days}

1 ordinary year=365 days1 \text{ ordinary year} = 365 \text{ days}

1 leap year=366 days1 \text{ leap year} = 366 \text{ days}

Total minutes=(Hours×60)+Minutes\text{Total minutes} = (\text{Hours} \times 60) + \text{Minutes}

💡Examples

Problem 1:

A school bus starts its journey at 7:15 a.m.7:15 \text{ a.m.} and reaches the school at 8:40 a.m.8:40 \text{ a.m.} Find the duration of the journey.

Solution:

  1. Write the end time: 8:40 a.m.8:40 \text{ a.m.}
  2. Write the start time: 7:15 a.m.7:15 \text{ a.m.}
  3. Subtract the minutes: 4015=25 minutes40 - 15 = 25 \text{ minutes}.
  4. Subtract the hours: 87=1 hour8 - 7 = 1 \text{ hour}.
  5. Total duration = 1 hour and 25 minutes1 \text{ hour and } 25 \text{ minutes}.

Explanation:

To find the duration, we subtract the start time from the end time. Since 4040 minutes is greater than 1515 minutes, we can subtract directly without borrowing.

Problem 2:

Convert 3 hours and 20 minutes3 \text{ hours and } 20 \text{ minutes} into total minutes.

Solution:

  1. We know that 1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes}.
  2. Multiply the hours by 6060: 3×60=180 minutes3 \times 60 = 180 \text{ minutes}.
  3. Add the remaining minutes: 180+20=200 minutes180 + 20 = 200 \text{ minutes}.
  4. Total = 200 minutes200 \text{ minutes}.

Explanation:

To convert hours to minutes, we use the multiplication rule (3×603 \times 60) and then add the extra minutes to get the final result.