Planning feasible journeys | Year 6

01 / LEARN

Understand the idea.

Work backwards from a deadline

A feasible journey fits all the stated times and requirements. Separate fixed clock times, such as an appointment, from durations, such as travel or check-in. Add every required duration before deciding when the journey must start.

For a latest-departure question, work backwards from the deadline. Subtract check-in time to find the latest arrival, then subtract travel time. A plan that meets the deadline exactly has no spare time if anything takes longer.

Check the complete journey

Check the complete outing, including travel out, activities, walks, waiting and travel home. Compare the total duration with the available time, then put the parts in order to confirm there are no overlapping activities or impossible connections.

Judge a plan against the actual goal. Earliest arrival, shortest travel time and largest time buffer are different goals. State any assumptions about exact travel times, and distinguish fitting exactly from leaving room for a delay.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Latest departure

An appointment begins at 10:15. Travel takes 35 minutes and check-in takes 10 minutes. When must you leave at the latest?

Worked solution

1
Combine the required preparation and travel.
$35 + 10 = 45 \min$
Both the journey and check-in must finish before the appointment begins.
2
Count backwards to a convenient hour.
$10:15 - 15 \min = 10:00$
This uses fifteen of the required forty-five minutes.
3
Subtract the remaining duration.
$\begin{aligned} 45 - 15 & = 30 \min \\ 10:00 - 30 \min & = 09:30 \end{aligned}$
The remaining thirty minutes bring the departure into the previous hour.
4
Check the plan forwards.
$\begin{aligned} 09:30 + 35 \min & = 10:05 \\ 10:05 + 10 \min & = 10:15 \end{aligned}$
The plan reaches the appointment exactly on time if both durations are as stated.

Answer

09:30, assuming travel takes exactly the stated time.

EXAMPLE 02

Fit an outing into a morning

An outing can run from 09:00 to 12:00. Travel out takes 30 minutes, a visit takes 60 minutes, a walk takes 15 minutes, a park stop takes 45 minutes and travel home takes 30 minutes. Does it fit?

Worked solution

1
Find the available duration.
$3 h = 3 \times 60 = 180 \min$
The time window from 09:00 to 12:00 is three complete hours.
2
Add every part of the outing.
$\begin{aligned} T & = 30 + 60 + 15 + 45 + 30 \\ = 180 \min \end{aligned}$
Both journeys and all three activities belong in the total.
3
Place the activities in order.
$\begin{array}{c} 09:00--09:30: travel out \\ 09:30--10:30: visit \\ 10:30--10:45: walk \\ 10:45--11:30: park \\ 11:30--12:00: travel home \end{array}$
Each activity begins when the previous one finishes, and the final journey ends at the deadline.
4
Calculate the time buffer.
$180 - 180 = 0 \min$
The outing fits exactly, with no allowance for delays.

Answer

It fits exactly, with no time buffer.

03 / YOUR TURN

Try it yourself.

Check your understanding

A 90-minute visit and two 20-minute journeys must fit into 2 hours. Is this possible?

Show answer & reasoning

No.

The visit and two journeys need $90 + 20 + 20 = 130$ minutes. Two hours provide $120$ minutes, so the plan exceeds the limit by $130 - 120 = 10$ minutes.

Keep practising

6 worksheet questions · 13 marks

Open worksheet Worked solutions

Read the questions online

A lesson starts at 14:20. Travel takes 25 minutes and settling in takes 5 minutes. Find the latest departure.
2 marks
A walk takes 18 minutes. A bus leaves at 11:25. If you leave home at 11:04, how much time is left before departure?
2 marks
An outing has parts lasting 25, 40, 15 and 30 minutes. It must fit into 2 hours. How much spare time is there?
2 marks
A trip begins at 09:00. Plan A takes a 30-minute bus, a 10-minute wait and a 15-minute walk. Plan B takes a 20-minute bus, a 25-minute wait and a 15-minute walk. Which arrives earlier, and by how much?
3 marks
You must be home by 14:00. A tour has return options arriving at 13:45 and 14:10. Which meets the deadline, and how much time does it leave?
2 marks
A plan lasts exactly 150 minutes, the whole available window. Give one reason it may be risky, and one sensible change.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A lesson starts at 14:20. Travel takes 25 minutes and settling in takes 5 minutes. Find the latest departure.
2 marks
$25 + 5 = 30$ minutes.
$14:20 - 30 minutes = 13:50$ .
13:50
A walk takes 18 minutes. A bus leaves at 11:25. If you leave home at 11:04, how much time is left before departure?
2 marks
$11:04 + 18 minutes = 11:22$ .
11:22 to 11:25 is 3 minutes.
3 minutes
An outing has parts lasting 25, 40, 15 and 30 minutes. It must fit into 2 hours. How much spare time is there?
2 marks
$25 + 40 + 15 + 30 = 110$ .
$120 - 110 = 10$ minutes.
10 minutes
A trip begins at 09:00. Plan A takes a 30-minute bus, a 10-minute wait and a 15-minute walk. Plan B takes a 20-minute bus, a 25-minute wait and a 15-minute walk. Which arrives earlier, and by how much?
3 marks
A takes 55 minutes and arrives at 09:55.
B takes 60 minutes and arrives at 10:00.
Plan A arrives 5 minutes earlier.
You must be home by 14:00. A tour has return options arriving at 13:45 and 14:10. Which meets the deadline, and how much time does it leave?
2 marks
13:45 is before 14:00.
14:10 is too late.
$14:00 - 13:45 = 15 minutes$ .
The 13:45 option, leaving 15 minutes.
A plan lasts exactly 150 minutes, the whole available window. Give one reason it may be risky, and one sensible change.
2 marks
There is no spare time.
A suitable change creates a buffer without ignoring a fixed appointment.
A delay could make the finish late. Shorten an optional activity or allow a longer window.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 6: itineraries, elapsed time and feasible journey planning, including connections and 24-hour time.

Official curriculum source ↗

In this lesson

Understand the idea.

Work backwards from a deadline

Check the complete journey

See the method in action.

Latest departure

Combine the required preparation and travel.

Count backwards to a convenient hour.

Subtract the remaining duration.

Check the plan forwards.

Fit an outing into a morning

Find the available duration.

Add every part of the outing.

Place the activities in order.

Calculate the time buffer.

Try it yourself.

Check your understanding

Keep practising