Maths Challenge #9 – Ring a–Ring a–Ringroad
The M25 motorway completely encircles London, and in Britain we drive on the left. So if you travel clockwise around the M25 you stay on the outside carriageway, whereas travelling anti-clockwise keeps you on the inside carriageway, which is shorter. But how much shorter?
The total length of the M25 is 188km (117 miles), so the advantage of being on the inside carriageway outght to be quite a lot – shouldn’t it?
Suppose that two cars travel around the M25, staying in the outside lane – one going clockwise and one going anti-clockwise. Also suppose that the distance between these two lanes is always 10 metres (to make it specific).
How much further does the clockwise van travel than the anti-clockwise one? You should also assume that the roads all lie in a flat plane.