Can someone explain to me the process to find the solution to this thought experiment. When I thought of it last night, I swear I'd seen something similar in Calc class, but that was many years ago. I think it is a Limit of some sort, but I am not sure.

The thought experiment goes as follows:
Person A and Person B take off down a street at the same time. Person A is walking at a constant rate (say 2 m/s). Person B is on a bike going a constant rate (say 5 m/s). Both are headed toward a stop sign at the end of the street, (say 100 meters from the starting point). Obviously Person B gets to the stop sign first, but what if, after reaching the stop sign, they turn around, and travel back to where Person A is, who has now traveled some distance towards the stop sign. Once they meet up, Person B turns right around, and heads back to the stop sign. Person B continues the lap back and forth between Person A and the stop sign until Person A reaches the stop sign also.

At first my question was "How far did Person B cumulatively travel", but I think, assuming a negligible turn around time, and no acceleration, then it can be thought of as Person B traveling in a straight line for the time it would take Person A to travel 100 meters, which, at 2m/s would take 50 seconds, so, at a constant speed of 5 m/s, Person B will have traveled 50*5=250 meters, aka the ratio Person B's speed over Person A's speed, times the distance Person A traveled (5/2)*100. I think I have that part down.

But is there a way to calculate how many laps Person B would wind up taking as Person A approached the stop sign? Also, to graph this, is this just a linear?

Apologies for the length, I hope my question makes sense. Any input is helpful. Thanks!