Weeds have taken over the paths. If mowed, they don't grow back, but unmowed weeds spread at speed $1$ along the road. What's the minimum speed of the mower to get rid of all the weeds? Roads are connected at each intersection.

[![enter image description here][1]][1] 

Source: [Here](https://puzzling.stackexchange.com/questions/115848/catch-the-invisible-and-omniscient-thief)'s a more cinematic, but mathematically equivalent formulation of the same puzzle.

  [1]: https://i.sstatic.net/fCrFym.png