Travel Graphs
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- Travel Graphs - Video - Travel Graphs Watch
Theory
A travel graph has time across and distance up. Each straight section has a speed \(=\) distance \(\div\) time: a car that goes \(30\) km in the first \(40\) minutes is doing \(30 \div \dfrac{2}{3} = 45\) km/h. This Year 8 maths page shows how to read and draw travel graphs.
Work out the scales first. If \(6\) squares cover \(30\) minutes, one square is \(5\) minutes. Do the same for the distance axis.
Reading a point: go up from the time to the line, then across. A point between grid lines is read as part of a square.
The shape: up is moving away, flat is stopped, down is coming back.
Speed of a section \(=\) distance \(\div\) time for that section; steeper means faster. From minutes to km/h, divide by the minutes and multiply by \(60\). A downward section still has a positive speed.
Average speed \(=\) total distance \(\div\) total time, counting stops. On a return trip count the distance out and back.
Two travellers: where the lines cross, they are at the same place at the same time; the gap straight up is how far apart they are. Coming towards each other, they close the gap at the sum of their speeds.
Drawing one: plot the (time, distance) point at the end of each stage and join the points with straight lines.
Speed from a section with the time in minutes:
| Section | Working | Speed |
|---|---|---|
| 6 km in 30 min | \(6 \div 30 \times 60\) | 12 km/h |
| 12 km in 30 min | \(12 \div 30 \times 60\) | 24 km/h |
| 15 km in 45 min | \(15 \div 45 \times 60\) | 20 km/h |
Finding the speed of a section
- Read the distance at the start and end of the section and subtract.
- Read the time taken.
- Divide distance by time, changing minutes to hours for km/h.
(i) Find the speed in the first \(40\) minutes.
(ii) Find the speed in the last \(40\) minutes.
| \(30 \div \dfrac{2}{3}\) | \(=\) | \(45\) |
| \((100 - 30) \div \dfrac{2}{3}\) | \(=\) | \(105\) |
(i) \(45\) km/h (\(40\) min \(= \dfrac{2}{3}\) h)
(ii) \(105\) km/h
(i) How far had it gone at 09:15?
(ii) How long did it stop?
(iii) Find its speed on the last section.
| \(60 - 30\) | \(=\) | \(30\) |
| \(30 \div 45 \times 60\) | \(=\) | \(40\) |
(i) Halfway between \(10\) and \(20\): \(15\) km
(ii) \(15\) min
(iii) \(40\) km/h
(i) Draw the travel graph.
(ii) Find the average speed for the whole trip.
Plot \((0, 0)\), \((45, 21)\), \((75, 21)\), \((120, 0)\) and join them.
| \(21 + 21\) | \(=\) | \(42\) |
| \(45 + 30 + 45\) | \(=\) | \(120 \text{ min}\) |
| \(42 \div 2\) | \(=\) | \(21\) |
(ii) \(21\) km/h. Each sail is \(28\) km/h; the wait pulls the average down.
(i) Find her speed on each section in m/s.
(ii) Write the faster speed in km/h.
| \(100 \div 40\) | \(=\) | \(2.5\) |
| \(300 \div 60\) | \(=\) | \(5\) |
| \(5 \times 3.6\) | \(=\) | \(18\) |
(i) Jog \(2.5\) m/s; sprint \(300\) m in \(60\) s \(= 5\) m/s
(ii) \(18\) km/h
(i) How far apart are they at 09:30?
(ii) When and where do they pass?
At 09:30 Zoe is \(2\) km from the pier and Hugo is \(8\) km.
| \(8 - 2\) | \(=\) | \(6\) |
(i) \(6\) km
(ii) Where the lines cross: 10:00, \(4\) km from the pier
Common pitfalls
Frequently asked questions
What does a flat line on a travel graph mean?
The traveller is stopped: time passes but the distance does not change.
How do I find speed from a travel graph?
Divide the distance covered in a section by the time it took.
Which section is fastest?
The steepest one.
What does it mean when two lines cross?
The two travellers are at the same place at the same time.
How do I find the average speed for a whole trip?
Divide the total distance travelled by the total time, including stops.