In terms of your distance, it says that bobby is klm due west of kym. If we denote negative values for due west and due south we get a distance equation that is:
D^2 = (x-bobby - x-kym)^2 + (y-bobby - y-kym)^2
Since bobby is walking east and starts at -klm due east (which is equivalent to klm due south), we get bobby-x = -klm + 3*t. Bobby's y co-ordinate doesn't change since we is walking purely in an east direction with no north or south component.
As for kym, she has no east or west component so kym-x = a. Since kym is travelling due south, kyms y component is b - 4*t where b is the initial y position.
So if kym starts at (a,b) then Bobby starts at (a-klm,b) and the distance is over time
D^2 = (a - (a-klm+3t))^2 + (b-4t-b)^2
= (klm-3t)^2 + (4t)^2
Now you can find the turning points that minimize this relationship.