Australian Curriculum v9 / ACiQ Year 8 Mathematics - Unit 3 - Duration and time zones

Duration and time zones

Solve duration and time-zone problems using 12-hour and 24-hour time, date changes and timetables.

Updated 2026-07-26 - 12 min read

Duration and time zones is taught here as a connected set of decisions, not a list of facts. Work through the prerequisite recall, explicit models, carefully faded examples, misconception repairs and transfer task before using the target in Check, Practice, Review or Rapid Revision.

This note is designed to work with the guided lessons, curated practice, flashcards, Tutor context, Review and Rapid Revision for the same canonical target. The same three evidence checks are used throughout, so feedback can route a learner back to the precise idea that needs repair.

Calculate elapsed time

Move through sensible time landmarks or use 24-hour time, accounting for hour boundaries and date changes. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by calculate elapsed time and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: Clock time uses base 60 and may cross noon, midnight or a new date, so direct decimal-like subtraction is unsafe.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 1.1

How long is it from 09:45 to 13:20?

Step 1 - identify the governing idea: Move through sensible time landmarks or use 24-hour time, accounting for hour boundaries and date changes.

Step 2 - apply it to this evidence: From 09:45 to 12:00 is 2 h 15 min and to 13:20 is another 1 h 20 min.

Result: 3 h 35 min

The relationship is visible in the working: From 09:45 to 12:00 is 2 h 15 min and to 13:20 is another 1 h 20 min. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 4 h 25 min — It does not agree with the required relationship: From 09:45 to 12:00 is 2 h 15 min and to 13:20 is another 1 h 20 min.
  • 3 h 75 min — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 2 h 35 min — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 1.2

A train leaves at 22:50 and arrives at 01:15 next day. Find duration.

Step 1 - identify the governing idea: Move through sensible time landmarks or use 24-hour time, accounting for hour boundaries and date changes.

Step 2 - apply it to this evidence: There are 1 h 10 min to midnight and 1 h 15 min after midnight.

Result: 2 h 25 min

The relationship is visible in the working: There are 1 h 10 min to midnight and 1 h 15 min after midnight. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 20 h 25 min — It does not agree with the required relationship: There are 1 h 10 min to midnight and 1 h 15 min after midnight.
  • 3 h 35 min — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 2 h 65 min — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 1.3

A film starts at 6:35 pm and lasts 145 minutes. When does it finish?

Step 1 - identify the governing idea: Move through sensible time landmarks or use 24-hour time, accounting for hour boundaries and date changes.

Step 2 - apply it to this evidence: 145 minutes is 2 h 25 min; adding gives 9:00 pm.

Result: 9:00 pm

The relationship is visible in the working: 145 minutes is 2 h 25 min; adding gives 9:00 pm. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 8:80 pm — It does not agree with the required relationship: 145 minutes is 2 h 25 min; adding gives 9:00 pm.
  • 9:20 pm — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 8:00 pm — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Convert between time zones

Express both locations relative to the same UTC reference, apply the signed offset and then adjust the date if midnight is crossed. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by convert between time zones and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: First convert the known local time to UTC, then convert UTC to the destination.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 2.1

It is 10:00 UTC. What time is it at UTC+10?

Step 1 - identify the governing idea: Express both locations relative to the same UTC reference, apply the signed offset and then adjust the date if midnight is crossed.

Step 2 - apply it to this evidence: Adding 10 hours gives 20:00, or 8:00 pm.

Result: 8:00 pm

The relationship is visible in the working: Adding 10 hours gives 20:00, or 8:00 pm. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 12:00 am — It does not agree with the required relationship: Adding 10 hours gives 20:00, or 8:00 pm.
  • 10:10 am — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 8:00 am — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 2.2

It is 3:00 pm at UTC+10. What time is it at UTC+8?

Step 1 - identify the governing idea: Express both locations relative to the same UTC reference, apply the signed offset and then adjust the date if midnight is crossed.

Step 2 - apply it to this evidence: The destination is two hours behind the known location.

Result: 1:00 pm

The relationship is visible in the working: The destination is two hours behind the known location. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 5:00 pm — It does not agree with the required relationship: The destination is two hours behind the known location.
  • 3:00 am — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 11:00 pm — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 2.3

At UTC−5 it is Monday 9:00 pm. What is the time at UTC+1?

Step 1 - identify the governing idea: Express both locations relative to the same UTC reference, apply the signed offset and then adjust the date if midnight is crossed.

Step 2 - apply it to this evidence: UTC+1 is six hours ahead, crossing midnight.

Result: Tuesday 3:00 am

The relationship is visible in the working: UTC+1 is six hours ahead, crossing midnight. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • Monday 3:00 pm — It does not agree with the required relationship: UTC+1 is six hours ahead, crossing midnight.
  • Monday 3:00 am — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • Tuesday 9:00 am — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Interpret timetables and schedules

Read departure, arrival, transfer and waiting times in sequence and distinguish elapsed travel time from local clock time. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by interpret timetables and schedules and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: Timetables may include time zones, overnight travel and waiting periods; all times must be put on a common timeline.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 3.1

A bus arrives at 10:20 and the connection leaves at 10:47. What is the wait?

Step 1 - identify the governing idea: Read departure, arrival, transfer and waiting times in sequence and distinguish elapsed travel time from local clock time.

Step 2 - apply it to this evidence: From 10:20 to 10:47 is 27 minutes.

Result: 27 min

The relationship is visible in the working: From 10:20 to 10:47 is 27 minutes. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 67 min — It does not agree with the required relationship: From 10:20 to 10:47 is 27 minutes.
  • 17 min — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 37 min — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 3.2

A flight departs 23:30 and lasts 4 h 45 min. What is the arrival clock time before time-zone adjustment?

Step 1 - identify the governing idea: Read departure, arrival, transfer and waiting times in sequence and distinguish elapsed travel time from local clock time.

Step 2 - apply it to this evidence: Adding 30 minutes reaches midnight, leaving 4 h 15 min.

Result: 04:15 next day

The relationship is visible in the working: Adding 30 minutes reaches midnight, leaving 4 h 15 min. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 03:75 — It does not agree with the required relationship: Adding 30 minutes reaches midnight, leaving 4 h 15 min.
  • 18:45 — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 04:15 same day — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 3.3

A class runs 08:55–10:10 with a 15-minute break included. How many teaching minutes occur?

Step 1 - identify the governing idea: Read departure, arrival, transfer and waiting times in sequence and distinguish elapsed travel time from local clock time.

Step 2 - apply it to this evidence: The full interval is 75 minutes; removing the 15-minute break leaves 60.

Result: 60 min

The relationship is visible in the working: The full interval is 75 minutes; removing the 15-minute break leaves 60. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 75 min — It does not agree with the required relationship: The full interval is 75 minutes; removing the 15-minute break leaves 60.
  • 90 min — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 45 min — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Retrieval check

Try these without looking back at the examples.

  1. A train leaves at 22:50 and arrives at 01:15 next day. Find duration.
  2. It is 3:00 pm at UTC+10. What time is it at UTC+8?
  3. A flight departs 23:30 and lasts 4 h 45 min. What is the arrival clock time before time-zone adjustment?

Answers

  1. 2 h 25 min — There are 1 h 10 min to midnight and 1 h 15 min after midnight.
  2. 1:00 pm — The destination is two hours behind the known location.
  3. 04:15 next day — Adding 30 minutes reaches midnight, leaving 4 h 15 min.

Transfer task

Find an unfamiliar example from school, daily life, a credible news source or another subject. Explain which of the three evidence checks applies. Complete the task, then audit your own response: identify the evidence used, the relationship applied, one plausible misconception and the final reasonableness check. If a peer could not reproduce your reasoning, add the missing step.

Sources