Time calculations, timetables and time differences
Keep clock readings separate from durations and put events on one timeline before calculating.
Core and Extended.
Before you begin
- Use multiples of sixty for seconds and minutes.
- Add and subtract signed numbers.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which 24-hour reading represents 7:05 p.m.?
What you will learn
- Convert between time units and 12-hour or 24-hour clocks.
- Calculate durations across midnight.
- Use stated time-zone offsets to compare local times.
A clock reading is not a duration
The clock reading 1515 is 3:15 p.m.; 0315 is 3:15 a.m. Noon is 1200 and midnight at the start of a day is 0000. In 12-hour notation these are 12 noon and 12 midnight; the a.m./p.m. boundary often causes confusion. Include the day when an event may cross midnight.
A duration measures elapsed time. One minute is sixty seconds, one hour is sixty minutes, one day is twenty-four hours and one week is seven days. Use the stated calendar information for months, since they have different lengths. When the syllabus problem assumes a year length, one year is 365 days unless a different calendar detail is given.
Convert with the unit relationship
A duration of 2 hours 18 minutes is 138 minutes or 2 + 18/60 = 2.3 hours. The decimal 2.18 hours is smaller and means two hours plus 10.8 minutes. To convert back, separate the whole hours and multiply the decimal fraction by sixty.
For a duration in seconds, divide by sixty for minutes and keep any remainder. For example, 190 seconds is three minutes ten seconds. For 1.25 days, multiply by twenty-four to get thirty hours. Track the unit at each stage, especially when a rate is measured per hour but the time is given in minutes.
Use a timeline for midnight and connections
A train leaving at 23:40 and arriving at 01:15 the next day travels for twenty minutes before midnight and seventy-five minutes after it: ninety-five minutes, or one hour thirty-five minutes. Directly subtracting the clock strings gives a negative answer because it ignores the change of day.
For a timetable connection, include walking or transfer time. Arrival at 10:48 with a required seventeen-minute transfer means the earliest feasible departure is 11:05. A departure at 11:02 is therefore too early, even though it comes after the arrival clock reading. Read any minimum connection or boarding condition.
Compare local times using a common reference
If City A is given as UTC+2 and City B as UTC+7, B's local clock is five hours ahead for that problem. To travel from an A departure time to a B arrival time, first convert the departure to B's clock, then add the duration. The given offsets are assumptions; real locations can have date-dependent clock changes.
A departure at 22:30 in A corresponds to 03:30 the next day in B. After a six-hour flight, arrival is 09:30 in B. For an elapsed-time calculation between two recorded local readings, convert both to the same reference and include their dates before subtracting. Local clock times alone can hide the actual duration.
Pause and explain
What duration does 1.6 hours represent?
Worked example
A train departs at 22:45 and arrives at 01:20 the next day. Find its journey time.
Show the worked solution
- From 22:45 to midnight is 1 hour 15 minutes.
- From midnight to 01:20 is 1 hour 20 minutes.
- Add to get 2 hours 35 minutes, or 155 minutes.
Answer 2 hours 35 minutes
From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Convert 2 hours 18 minutes to minutes and decimal hours.
Give me a hint
Use sixty minutes per hour in both directions.
Compare my reasoning
- Two hours is 120 minutes, so the total is 138 minutes.
- Eighteen minutes is 18/60 = 0.3 hour.
- The duration is 2.3 hours, checked by 2.3 × 60 = 138.
138 minutes; 2.3 hours
Look for these in your work
- Used a base of sixty for the minute conversion.
- Checked the decimal-hour value in reverse.
A coach leaves at 23:50 and arrives at 02:25 the following day. Find the duration, and express the arrival in 12-hour notation.
Give me a hint
Split the journey at midnight.
Compare my reasoning
- There are ten minutes to midnight.
- After midnight there are 2 hours 25 minutes; total duration is 2 hours 35 minutes.
- The arrival is 2:25 a.m., on the following day.
2 hours 35 minutes; 2:25 a.m. the next day.
Look for these in your work
- Included the day boundary.
- Used the correct a.m. label after midnight.
City A is UTC+2 and City B is UTC+7 throughout this fictional journey. A flight leaves A at 22:30 on Monday and takes six hours. Find the local arrival day and time in B.
Give me a hint
B is five hours ahead; convert the departure before adding flight time.
Compare my reasoning
- Monday 22:30 in A is Tuesday 03:30 in B.
- Add six hours to get Tuesday 09:30.
- Check in UTC: departure Monday 20:30, arrival Tuesday 02:30, then add B's seven hours.
Tuesday 09:30 in City B
Look for these in your work
- Put the clocks on one common reference.
- Carried the day change through both calculations.
Common mistakes
- Treating minutes as hundredths of an hour.
- Ignoring the day when subtracting local clock readings.
- Adding a time-zone difference in the wrong direction.
What can you explain now?
An arrival is 10:48 and the transfer takes at least 17 minutes. What is the earliest feasible departure?
Compare with the explanation
11:05
Add twelve minutes to 11:00 and five more minutes for the full transfer.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Calculate the duration from 23:35 to 01:10 the next day. Explain how you would compare two arrival readings from different time zones.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.
Original StudyForA teaching content · AI-assisted checks · Human teacher review pending.
Number contains 19 sequenced lessons; Algebra and graphs contains 21; Coordinate geometry contains 10 teaching lessons and a mixed checkpoint. Nine earlier overviews support selected topics across the syllabus. The other six syllabus areas, full cumulative assessment and human teacher review are not yet complete. Written lesson practice is self-checked, not automatically graded. The checkpoint samples skills and does not save an exam grade or certify mastery.
Check the official syllabus 2025–2027 Open related practice and resources