USING CALC: answer how far ships are (details below)?

Question

At midnight Ship B was 90 miles south of Ship A. Ship A sailed east at 15 miles/hr and SHip B sailed north at 20 miles per hour. At what time were the two ships closest? (Hint: When the distance between two objects is at a minimum, the square of the distance is also at a minimum)

Answer 1

Take as reference the position ofA and a Coordinate system with y axis S-N and x axis
W-E
Y(B) = 90 -20 t
X(A) = 15t
d^2= (90-20t)^2+(15t)^2
(d^2)´= 2(90-20t)(-20) +450t =0
t= 3600/1250=2h52min48seg (a.m)