Decide when you want the person to start walking, calculate the difference between start time and current time, apply the distance function for that many time increments. it's not real, you don't actually have to update the record in realtime, you could record an ending time right when they start, because you'll know how long it took them to go that far. (assuming we're talking about no obstacles, no change in direction, "as the crow flies" kind of math)

basically, treat the whole thing like it already happened, and your results are just saying "where were they at any given point in time"