One athlete in a race running on a long, straight
track with a constant speed v, is a distance d behind a sec-
ond athlete running with a constant speed u. (a) under
what circumstances is the first athlete able to overtake the
second athlete? (b) find the time t it takes the first ath-
lete to overtake the second athlete, in terms of d, v,, and
vy. (c) at what minimum distance d, from the leading
athlete must the finish line be located so that the trailing
athlete can at least tie for first place? express d, in terms
of d, v1, and v, by using the result of part (b).