At noon, one ship A was directly north of another ship B. Ship A was sailing south at 30kph and B was sailing east at 15kph. After how many hours will the two ships be nearest each other?

Answer 1

at time t hours after noon, we have the distance (starting at k km) is

z^2 = (k-30t)^2 + (15t)^2
2z dz/dt = -60(k-30t) + 450t
dz/dt = (2250t-60k)/(2z) = 15(75t-2k)/z

dz/dt=0 when t = 2k/75

so it depends on how far apart the ships were at noon.