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Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?

### There and Back

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

### Escalator

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?

##### Stage: 4 Challenge Level:

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 graphs?
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?