E1.15 Time
- Syllabus
- 0580–2028–2029
- Topic
- E1.15
- Level
- Extended
Learning objectives
E1.15.1Calculate with time: seconds (s), minutes (min), hours (h), days,• Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.E1.15.2Calculate times in terms of the 24-hour and 12-hour clock.• Calculate times in terms of the 24-hour and 12-hour clock.E1.15.3Read clocks and timetables• Read clocks and timetables. 1 year = 365 days. In the 24-hour clock, for example, 3.15 a.m. will be denoted by 03 15 and 3.15 p.m. by 15 15. Includes problems involving time zones, local times and time differences.
Calculate across units of time
Time units do not use one place-value system. Convert through the exact relationship between neighbouring units, multiplying toward smaller units and dividing toward larger units.
| Relationship | Toward the smaller unit | Toward the larger unit |
|---|---|---|
| 1 minute = 60 seconds | minutes × 60 | seconds ÷ 60 |
| 1 hour = 60 minutes | hours × 60 | minutes ÷ 60 |
| 1 day = 24 hours | days × 24 | hours ÷ 24 |
| 1 week = 7 days | weeks × 7 | days ÷ 7 |
| 1 year = 12 months | years × 12 | months ÷ 12 |
For day calculations in this syllabus, use 1 year = 365 days unless the question supplies other information.
July has 31 days, so it contains 31×24×60×60=2678400 seconds. For 2.15 hours, multiply the whole decimal by 60: 2.15×60=129 minutes.
For a mixed-unit answer, convert to the smallest useful unit first. Eighteen trips of 23 minutes total 414 minutes; 414÷60=6 remainder 54, so the time is 6 hours 54 minutes.
A decimal hour is not hours and minutes: 2.15 hours is 2 hours 9 minutes, not 2 hours 15 minutes. Months have different numbers of days, so do not invent a fixed month-to-day conversion unless the question provides one.
Calculate with 12-hour and 24-hour times
Clock times name positions in a day; durations measure the interval between them. Convert both clock formats consistently, then add, subtract or bridge midnight in hours and minutes.
| 12-hour time | 24-hour time | Rule |
|---|---|---|
| 3.25 a.m. | 03 25 | keep the hour and add a leading zero |
| 3.25 p.m. | 15 25 | add 12 to the hour |
| 12.00 noon | 12 00 | noon starts the p.m. half of the day |
| 12.00 midnight | 00 00 | midnight starts a new day |
To add a duration, add minutes first and exchange every 60 minutes for 1 hour. Starting at 19 50, adding 2 hours 42 minutes gives 21 92, which normalises to 22 32.
For an interval across midnight, split at 24 00. From 21 15 to 24 00 is 2 hours 45 minutes; from 00 00 to 04 33 is 4 hours 33 minutes. The total is 7 hours 18 minutes.
To find a start time, reverse the process and borrow 1 hour as 60 minutes when necessary. A film ending at 23 05 after 2 hours 50 minutes started at 20 15.
Do not subtract clock digits as ordinary base-10 numbers. There are 60 minutes in an hour, and 24 00 is the same boundary instant as 00 00 on the next day.
Read timetables and solve time-zone journeys
A timetable links places or events to clock times. Read the correct row and column first; then distinguish travel time, waiting time and local-time differences.
For each stage, pair its departure with its arrival. A boat departing Millwater at 11 45 and arriving Westbridge at 13 07 travels for 1 hour 22 minutes. A wait between an arrival and the next departure is not travel time, but it is included if the question asks for the whole journey.
| Statement | Conversion at the same instant |
|---|---|
| destination is k hours ahead | destination time = source time + k hours |
| destination is k hours behind | destination time = source time − k hours |
For a flight: 1. Start with the departure day and local time. 2. Add the flight duration in the departure time zone. 3. Apply the destination's ahead/behind offset. 4. Move the day or date whenever the running time crosses 24 00 or 00 00.
A plane leaves Seattle at 07 30 on Tuesday, flies for 10 hours 55 minutes, and Seoul is 16 hours ahead. In Seattle time it lands at 18 25 Tuesday; adding 16 hours gives 10 25 Wednesday in Seoul.
A time-zone offset changes the local clock label, not the flight duration. Do not add the offset to the elapsed flying time, and always state the new day or date after a midnight crossing.