The idea, step by step
Keep each part of a journey
A journey with connections includes time in vehicles and time waiting between them. Make a short timeline: depart, arrive, next depart, final arrive. Calculate each interval using the same local clock or convert time zones first.
If a bus arrives at 08:42 and a train leaves at 08:50, the wait is 8 minutes. That time belongs in the total journey even though the passenger is not moving. A direct check is final arrival minus first departure.
| Leg | Departure | Arrival |
|---|---|---|
| Bus to station | 08:15 | 08:42 |
| Train to city | 08:50 | 09:27 |
A connection needs more than a positive gap
A transfer may require walking between platforms or checking in. If the stated minimum is 6 minutes, a 5-minute gap does not work even though the next service has not yet left. Use “at least” carefully: an exactly 6-minute gap satisfies a minimum of 6 minutes.
When choosing between services, work backwards from the required arrival or forwards from when travel can start. Include the transfer rule and any given delay. Explain your choice using the timetable rather than assuming the fastest single leg gives the fastest whole journey.
A common trap
Add the two travel times but ignore the time between services.
Instead: Total elapsed journey time includes all waiting. Compare first departure with final arrival as a check.
See the thinking
Travel plus waiting
Use the morning timetable to find bus time, waiting time, train time and total journey time.
| Leg | Departure | Arrival |
|---|---|---|
| Bus | 08:15 | 08:42 |
| Train | 08:50 | 09:27 |
- Bus: 08:42−08:15=27 min.
- Wait: 08:50−08:42=8 min.
- Train: 09:27−08:50=37 min.
- Total=27+8+37=72 min; 08:15 to 09:27 also gives 72 min.
A transfer rule
A bus reaches a station at 16:32. Trains leave at 16:37 and 16:52. At least 6 minutes are needed to transfer. Which train is the first possible one?
- The 16:37 train gives 5 min, less than 6.
- The 16:52 train gives 20 min, so it is possible.
Check your understanding
A bus arrives at 09:18; a train departs at 09:25. Is a 7-minute minimum transfer satisfied?
Show answer
Yes, exactly.
09:25−09:18=7 minutes, which meets “at least 7”.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- A bus leaves at 07:40 and arrives at 08:12. Find the travel time.2 marks
- You arrive at 10:46 and the next service leaves at 11:05. Find the waiting time.2 marks
- Leg 1 takes 28 min, the wait is 12 min and leg 2 takes 35 min. Find total time.2 marks
- Arrival is 14:24. Departures are 14:29, 14:36 and 14:50. A transfer needs at least 8 min. Choose the first possible departure.2 marks
- A service arrives at 12:20 after travelling for 45 minutes. Its departure stop is a 10-minute walk from home. What is the latest time to leave home if no extra boarding time is needed?2 marks
- A journey starts at 08:10, includes 25 min travel, 15 min wait and 40 min travel. Find arrival and check total time.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A bus leaves at 07:40 and arrives at 08:12. Find the travel time.2 marks
20 min to 08:00+12 min=32 min.
32 min. - You arrive at 10:46 and the next service leaves at 11:05. Find the waiting time.2 marks
14 min to 11:00+5 min=19 min.
19 min. - Leg 1 takes 28 min, the wait is 12 min and leg 2 takes 35 min. Find total time.2 marks
28+12+35=75.
75 min, or 1 h 15 min. - Arrival is 14:24. Departures are 14:29, 14:36 and 14:50. A transfer needs at least 8 min. Choose the first possible departure.2 marks
14:29 allows 5 min and fails; 14:36 allows 12 min and works.
14:36. - A service arrives at 12:20 after travelling for 45 minutes. Its departure stop is a 10-minute walk from home. What is the latest time to leave home if no extra boarding time is needed?2 marks
Service departure=12:20−45 min=11:35.
Leave home 10 min earlier: 11:25.
11:25. - A journey starts at 08:10, includes 25 min travel, 15 min wait and 40 min travel. Find arrival and check total time.2 marks
25+15+40=80 min.
08:10+1 h 20 min=09:30.
09:30; total 80 min.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Converting 12-/24-hour time; elapsed time across midnight; timetables and journeys; time-zone differences; date changes; checking real-world scheduling answers.
Official curriculum source ↗