One athlete in a race running on a long, straight track with a constant speed $v_{1}$ is a distance $d$ behind a second athlete running with a constant speed $v_{2} .$ (a) Under what circumstances is the first athlete able to overtake the second athlete? (b) Find the time $t$ it takes the first athlete to overtake the second athlete, in terms of $d, v_{1}$, and $v_{9}$. (c) At what minimum distance $d_{2}$ from the leading athlete must the finish line be located so that the trailing athlete can at least tie for first place? Express $d_{2}$ in terms of $d, v_{1}$, and $v_{2}$ by using the result of part (b).