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Answer: 500 metres


80 spokes = 4 miles
80 $\times$ radius = 4 miles
20 $\times$ radius = 1 mile
20 $\times$ radius $\approx$ 1600 metres
         radius $\approx$ 80 metres
circumference $\approx$ 160$\pi$ metres
                      $\approx$ 500 metres


This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.