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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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Parabolic Patterns

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

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More Parabolic Patterns

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.

Bus Stop

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3




Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other.

At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4; the one leaving Shipton is faster (It has a bigger engine!). The buses travel to and fro between the towns .

They meet for the second time at the 145th milestone and for the third time at the 201st milestone. What milestones are at Shipton and Veston?