I don't have a specific problem but I have a general question about related rates. I understand how to set everything up, use implicit differentiation, and solve for the desired variable, but I am unsure how to tell if the rates of change are negative or positive.

Here's an example that I do know how to do. Let's say Car A is approaching the south and Car B is moving to the east. When I draw the picture, I know that dy/dt is negative because Car A is moving in a negative direction and that dx/dt is positive.

But let's say that Car B is approaching the west instead of the east, and that Car A is still moving south. Would both dy/dt and dx/dt be negative? Or is it just dy/dt? Or neither? This is the only part of the problem that I'm unsure of. And if I were to find dz/dt, would I expect the value to be negative since the two cars are approaching each other?

Thanks for clarifying this for me.