Question

A boat leaves a dock at 2:00 P.M. and travels due south at a speed of 25 km/h. Another boat has been heading due east at 30 km/h and reaches the same dock at 3:00 P.M. How many minutes past 2:00 P.M. were the boats closest together? minutes

Answer 1

Y = 25 T distance first boat travels south in T hours

X = 30 - 30 T distance second boat is from dock at T = 1 hr

D = (X^2 + Y^2)^1/2 distance boats are apart

2 D dD / dT = d / dt (625 T^2 + 900 - 60 T + 900 T^2)

2 D dD / dT =3050 T - 60 = 0

T = 6 / 305 hrs = .0196 hrs = 1.18 min