A boat leaves a dock at 2:00 P.M. and travels due south at a speed of 15 km/h. Another boat has been heading due east at 20 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?

Answer 1

as usual, draw a diagram. The distance z between the boats at time t hrs after 2:00 is

z^2 = (15t)^2 + (20-20t)^2
2z dz/dt = 2(15t)(15) + 2(20-20t)(-20)
z dz/dt = 1250t - 800

clearly dz/dt=0 when t=8/1250 hours

Now just change that to a time of day.