### Lifeboat Rescue Analysis

Suppose a ship is searching visually for a life raft and that at time t, range is r(t) and detection rate is gamma(t) = 40 / r(t)^3 hr^-1, with t in hours, and r(t) in nm. The ship starts the search at an initial range of 2 nm and approaches the life raft on a direct course at a speed of 10 knots. Answer the following: