Here are the same reference frames with the distances specifically marked. It's really very simple: Jane is at O and Spot is 28 meters meters away from her, to the right (i.e. along the x-direction). If Dick is at O', 10 meters from Jane, then Spot must be 18 meters from him. Dick' reference frame (and Dick) is presently 10 meters from Jane because he left the point where Jane was (O), and has been moving along x at 2 m/s for the last 5 seconds.
As a formula, x' = x - s, and since s = v t it follows that x' = x - v t.
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