One athlete in a race running on a long, straight track with a constant speed V1 is a distance d behind a second athlete running with a constant speed V2. At what maximum distance from the leading athlete must the finish line be located so that the trailing athlete can at least tie for the first place?
first runner runs distance (x+d)
second runner runs x
time = distance / speed
both the same time
x / V2 = (x+d) /V1
V1 x = V2 x + V2 d
(V1-V2) x = V2 d
x = V2 d / (V2-V1)