Time
Section: Number 2 | Syllabus: Cambridge IGCSE Mathematics (0580)
Units of Time and the 24-Hour Clock
Time is measured in a mix of units that don't follow the usual base-10 pattern, and can be written in either 12-hour or 24-hour format. Converting confidently between all of these is the foundation for every other time calculation.
- Key relationships: 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day, 7 days = 1 week, 12 months = 1 year, and (for calculation purposes) 1 year = 365 days
- To convert a pm time (other than 12 pm) to 24-hour format, add 12 to the hour
- To convert a 24-hour time of 13:00 or later back to 12-hour format, subtract 12 from the hour and label it pm
Worked Example: Converting Between 12-Hour and 24-Hour Clock
- 9:40 pm in 24-hour clock: 9 + 12 = 21, so 21:40
- 06:05 in 12-hour clock: 6:05 am (no adjustment needed before noon)
- 14:50 in 12-hour clock: 14 - 12 = 2, so 2:50 pm
Worked Example: Converting Between Units of Time
- 4 hours 25 minutes in minutes: 4 × 60 + 25 = 265 minutes
- 320 seconds in minutes and seconds: 320 ÷ 60 = 5 remainder 20, so 5 minutes 20 seconds
Common Mistakes
MistakeForgetting to add 12 when converting a pm time to 24-hour format, e.g. writing 9:40 pm as 09:40
Fixevery pm time except 12 pm needs 12 added to the hour: 9:40 pm = 21:40
MistakeConfusing 12:00 midnight with 12:00 noon
Fixmidnight is 00:00 in 24-hour format (the very start of the day), while noon is 12:00 - they are 12 hours apart
Timetables, Durations and Time Zones
Adding a duration to a 24-hour time can carry past both 60 minutes and 24 hours. Time zone problems add a further shift on top of this, so keeping the time "unwrapped" until the last step avoids confusion about which day is involved.
- When adding a duration, add the hours and minutes separately first, then carry any full hour from a minutes total of 60 or more
- If the resulting time reaches 24:00 or beyond, subtract 24:00 - this means the event happens on the next day
- For time zone problems, add or subtract the zone difference - it often helps to do this before wrapping the time back into the normal 00:00–23:59 range
Worked Example: Adding a Duration in 24-Hour Time
- Question: A flight departs at 22:35 and takes 9 hours 50 minutes. Find the arrival time, and state whether it arrives the next day.
- Step 1: Add hours and minutes separately: 22 + 9 = 31, 35 + 50 = 85
- Step 2: 85 minutes is 1 hour 25 minutes, so carry the hour: 31 + 1 = 32 hours, 25 minutes
- Step 3: 32:25 is past 24:00, so subtract 24 hours: 32 - 24 = 8
- Answer: 08:25, the next day
Worked Example: Combining a Duration with a Time Zone Change
- Question: A flight departs from Singapore at 23:15 and takes 13 hours 40 minutes. Singapore local time is 13 hours ahead of Los Angeles local time. Find the local time in Los Angeles when the flight arrives.
- Step 1: Add the duration without wrapping past 24:00 yet: 23:15 + 13:40 = 36:55
- Step 2: Subtract the 13-hour zone difference from this unwrapped time: 36:55 - 13:00 = 23:55
- Step 3: Since 23:55 is under 24:00, this is Los Angeles local time on the same day the flight departed
- Answer: 23:55
Common Mistakes
MistakeWrapping the time back into the 00:00–23:59 range too early, before applying a time zone adjustment, causing confusion about which day is involved
Fixkeep the time in its "unwrapped" form (allowing hours past 24) until every addition and subtraction is finished, then wrap once at the very end
MistakeAdding minutes without carrying when the total reaches 60 or more, e.g. writing 22:85 instead of 23:25
Fixwhenever the minutes total reaches 60, subtract 60 from the minutes and carry 1 to the hours: 85 minutes = 1 hour 25 minutes
Interactive revision notes, videos and practice questions load below.