I am reading about an algorithm. For a part of it, to present the underlying logic uses the following analogy which I do not understand:
If two people run on a track and one of them runs with twice the speed of the other, they will meet at the start of the next round. Now if we assume that the QuickRunner had a head start of $k$ meters on a $n$ step round when will they meet? They will meet $k$ meters before the start of the next lap since QuickRunner would do $k+2(n-k)$ steps, and the slow one would have done $n-k$ steps. So both will be $k$ steps before the start of the loop.
I don't see why they would meet $k$ steps before the start of the loop.
Could you please help understand this?