At t = 0, one athlete in a race running on a long, straight track with a constant speed υ1 is a distance d1 behind a second athlete running with a constant speed υ2. (a) Under what circumstances is the first athlete able to overtake the second athlete? (b) Find the time t at which the first athlete overtakes the second athlete, in terms of d1, υ1, and υ2. (c) At what minimum distance d2 from the leading athlete must the finish line be located so that the trailing athlete can at least tie for first place? Express d2 in terms of d1, υ1, and υ2 byusing the result of part (b).

At t = 0, one athlete in a race running on a long, straight track with a constant speed υ₁ is a distance d₁ behind a second athlete running with a constant speed υ₂. (a) Under what circumstances is the first athlete able to overtake the second athlete? (b) Find the time t at which the first athlete overtakes the second athlete, in terms of d₁, υ₁, and υ₂. (c) At what minimum distance d₂ from the leading athlete must the finish line be located so that the trailing athlete can at least tie for first place? Express d₂ in terms of d₁, υ₁, and υ₂ by
using the result of part (b).