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Pentagonal

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?

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Swimmers

Swimmers in opposite directions cross at 20m and at 30m from each end of a swimming pool. How long is the pool ?

On the Road

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

Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12:30, then met the bike at 13.00 and the motorcycle at 13.30. The motorcycle met the scooter at 13.45 then it overtook the bike at 14.00. At what time did the bike and the scooter meet?