I am given this related rates problem here which says:
"Car $A$ is $1$ km west of car $B$ . Car $A$ starts to travel North at a rate of $30$ km/h, and $6$ minutes later, car $B$ starts to travel south at a rate of $50$ km/h. At what rate is the distance between the two cars changing $10$ minutes after car $A$ starts moving?"
My work with the diagram is above. I would post it here but I'm not really sure how to draw diagrams out with LaTeX so I figured I would just post a link.
Could someone please tell me if I am going about this the right way? Thanks!
You're missing including the time dependence. The distance between $A$ and $B$ at any given point in time is
$$d(t)=\sqrt{d_{0,x}^2+(d_{0,y}+v_At+v_Bt)^2},$$ where $v_i$ is the speed of car $i$ and $d_{0,x}$ is the initial separation in the west-east direction (here $1$ km) and $d_{0,y}$ is the initial separation in the north-south direction ($3$ km).
Now differentiate $d(t)$ w.r.t. time and evaluate the resulting expression at $t=10$ minutes (but be careful about units) to get your answer.