Travel Graphs
A travel graph, or distance–time graph, shows how far someone is from their starting point as time passes. In NSW Year 7 maths, students learn to read the story a graph tells and to work out speeds from it (NESA outcome MA4‑RAT‑C‑01).
You will read distances and times from points, explain what an upward, flat or downward section means, calculate the speed of each section and compare steepness, find the average speed for a whole trip including stops, and spot where two travellers meet. A family drive to a lake and back is a typical example. This subtopic is part of Year 7 Ratios, Rates and Time.
Every question with a fully worked solution.
- Travel Graphs - Video - Distance Time Graphs Watch
Theory
A travel graph (a distance-time graph) shows how far someone is from their starting point as time goes by. A line going up means moving away, a flat line means stopped, and a line going down means coming back. The steeper the line, the faster the speed. This Year 7 maths page shows how to read, draw and find speeds from travel graphs.
Time goes across the horizontal axis. Distance from the start goes up the vertical axis. Always read the axis labels and units first.
Reading a point. Go up from the time to the line, then across to the distance axis. If the time axis shows clock times, count on between them to find the time taken.
Reading the shape. A line going up means moving away. A flat line means stopped: time passes but the distance does not change. A line going down means coming back towards the start.
Speed of a section \(=\) distance \(\div\) time, using the two ends of the section. The steeper the line, the faster. For km/h, change minutes to hours first (\(30\) min \(= 0.5\) h, \(45\) min \(= 0.75\) h). For m/s, use metres and seconds: \(120\) m in \(15\) s is \(8\) m/s, and \(8 \times 3.6 = 28.8\) km/h.
Average speed for a whole trip \(=\) total distance \(\div\) total time, with the stops included.
Two travellers on one graph. Where the two lines cross, they are at the same place at the same time.
What the line tells you:
| The line ... | means ... |
|---|---|
| goes up | moving away |
| is flat | stopped |
| goes down | coming back |
| is steeper | faster |
| is less steep | slower |
How to find the speed of a section
- Read the distance and the time at both ends of the section.
- Subtract to find the distance and the time for that section.
- Change minutes to hours (for km/h).
- Divide: speed \(=\) distance \(\div\) time.
How to draw a travel graph
- Write a point (time, distance) for the end of each stage.
- Plot the points, starting at \((0, 0)\), and join them with straight lines.
(i) How far from home is he after \(10\) min?
(ii) At which two times is he \(600\) m from home?
(iii) How long does he stay?
(i) Up from \(10\) min to the line, then across: halfway to \(1000\) m.
(ii) Across from \(600\) m, the line is met twice: on the way out at \(12\) min, and on the way back at \(48\) min.
(iii) The flat section runs from \(20\) min to \(40\) min.
| \(40 - 20\) | \(=\) | \(20\) |
(i) \(500\) m
(ii) \(12\) min and \(48\) min
(iii) \(20\) min
| \(16 \div 0.8\) | \(=\) | \(20\) |
| \(12 \div 0.4\) | \(=\) | \(30\) |
A: \(16\) km in \(48\) min \(= 0.8\) h, so \(20\) km/h. B: flat, so stopped (\(0\) km/h). C: \(28 - 16 = 12\) km in \(84 - 60 = 24\) min \(= 0.4\) h, so \(30\) km/h. C is fastest (the steepest).
(i) Draw the travel graph.
(ii) Find his speed home.
(i) The points are \((0, 0)\), \((40, 12)\), \((60, 12)\) and \((90, 0)\), joined with straight lines:
| \(12 \div 0.5\) | \(=\) | \(24\) |
(ii) \(12\) km in \(0.5\) h: \(24\) km/h.
(i) Find the speed each way.
(ii) Find the average speed for the whole trip.
| \(90 \div 1.5\) | \(=\) | \(60\) |
| \(90 \div 1\) | \(=\) | \(90\) |
| \(180 \div 4\) | \(=\) | \(45\) |
(i) \(60\) km/h out and \(90\) km/h back
(ii) \(45\) km/h (total distance \(\div\) total time, with the stop), not \((60 + 90) \div 2 = 75\).
(i) Find each speed.
(ii) When and where do they pass?
| \(80 \div 4\) | \(=\) | \(20\) |
| \(80 \div 1\) | \(=\) | \(80\) |
(i) Cyclist \(20\) km/h, driver \(80\) km/h.
(ii) Where the lines cross: about 09:36, \(32\) km from town A. (Check: the cyclist rides \(20 \times 1.6 = 32\) km in \(1.6\) h.)
| \(120 \div 15\) | \(=\) | \(8\) |
| \(8 \times 3.6\) | \(=\) | \(28.8\) |
\(8\) m/s, which is \(28.8\) km/h.
Common pitfalls
Frequently asked questions
What does a flat line on a travel graph mean?
The person is stopped: time passes but the distance does not change.
How do you find speed from a travel graph?
Divide the distance for a section by the time for that section.
What does a steeper line mean?
A faster speed: more distance in the same time.
How do you find the average speed for a whole trip?
Divide the total distance by the total time, including stops.
What does it mean when two lines cross?
The two travellers are at the same place at the same time.