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On the Road

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?

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Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

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A Scale for the Solar System

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

Speed-time Problems at the Olympics

Stage: 4 Challenge Level: Challenge Level:1





At the 2012 Olympic games, the qualifying standards for the women's 100 metres race was 11.29s. How does this compare with the speed of a bus?




At the 2012 Olympics Shelly-Ann Fraser-Pryce won the women's 100m in a time of 10.75s. If she had continued running, how much further would she have run by the time an athlete running at the qualifying speed (11.29s) would have crossed the line?



In the 2009 IAAF World championship, Usain Bolt ran the 100m in 9.58s. Estimate how far he would have been ahead of the gold medallist from Lane 2 had they been racing together.





Imagine that you raced in the 200m with Usain Bolt. By what length would he beat you?




Imagine that a 2km rowing race took place on a rowing lake with two separate legs of 1km. How would the total race time vary from a race on a river where one leg is upstream and the other downstream?



Imagine that cyclist A completes a lap following the blue line on the velodrome track. Cyclist B completes a lap 1m inside the blue line and cyclist C completes a lap 2m outside the blue line. How do the distances travelled vary between the cyclists?



In the past, the start of a 100m race was indicated by a pistol shot next to lane 1. Did this give a significant advantage to the runner in lane 1? Would it have given a significant advantage to anyone if this pistol was fired from the end of lane 4?


Imagine an announcement is made from a podium in the centre of a stadium. As the speaker talks into her microphone the sound is simultaneously sent to speakers which project the sound into the stadium and up to satellites which transmit the signal as digital radio. Who might hear the sound first: someone listening on the radio or someone listening in the stadium?


Note: In this problem you might not have been given all of the required data and you might need to make estimates or approximations. You should be clear in your mind as to any assumptions that you make whilst constructing your answers.