Question

A boat leaves a dock at 3:00 P.M. and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 4:00 P.M. How many minutes after 3:00 P.M. were the two boats closest together? (Round your answer to the nearest minute.)

Answer 1

\[d=\sqrt{625t ^{2}-450t+225}\] differentiate and set to 0, solve for minimum.\[5(25t-9)\over \sqrt{25t ^{2}-18t+9}\]

Answer 2

t=9/25
t=(9/25)60=21.6 min or 3:22 PM