M25 Quiz Puzzle Answer

When it opened the M25 was the longest ring road in Europe, completely encircling London. In the UK we drive on the left, so going clockwise around the M25 you drive on the outside carriageway, and going anticlockwise you drive on the inside carriageway.

So it is shorter to drive around the M25 in an anticlockwise direction than in a clockwise direction. But how much shorter? The M25 is 117 miles long, so surely there is quite a big difference.

Assume two white vans drive around the M25 in opposite directions, and being white vans they stay in the fast lane in the middle of the motorway. For the sake of simplicity the two lanes are always ten metres apart, and the motorway is on a flat plain.

What is the difference between the two vans' journeys?

If the M25 were circular then the difference between the two journeys would be 20π metres, but does this still hold for the irregular route of the M25?

Well, actually it does. Any irregular polygon can be represented by straight lines and curves. The difference between journeys along parallel straight lines is zero, and the curves cancel each other out to leave a circle.

So just over 60 metres is the answer.


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