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'Four on the Road' printed from http://nrich.maths.org/
Caroline sets out in her car on a journey. Scott is out on his
scooter that afternoon too. Each of these graphs represents a
journey they could make. The horizontal axis shows the number of
minutes that have passed since noon, and the vertical axis shows
the distance each vehicle is from Caroline's house.
Can you tell a story for each of the journeys shown in the
What is the same about each journey? What is different?
You may wish to use words like speed, direction, distance, time,
overtake, and meet.
Caroline and Scott also see Muna on her motorbike and Bill on his
bike that afternoon.
Here are five statements about all their journeys.
- Caroline overtook Scott at 12:30pm
- Caroline met Bill at 1pm
- Caroline met Muna at 1:30pm
- Muna met Scott at 1:45pm
- Muna overtook Bill at 2pm
Sketch graphs which represent each statement. Are there other
graphs you could have drawn? How much freedom do you have? What
extra statements could you add to reduce this freedom and specify
the graphs more exactly?
Can you draw a graph showing all four vehicles which satisfies all
five statements at the same time?