Finding the optimal path across two point with varying speed

[labyrinthus]

Homework Statement

[PLAIN]http://img214.imageshack.us/img214/194/calcdr.jpg [Broken]
I need to find the optimal path across two points, in two straight line segments. The speed from point A to B is 12ft/s, and 4ft/s from point B to C.

Homework Equations

The Attempt at a Solution

I set segment AB as x, BC as y, ED as w, and DC as z. With that, I set up the equations:

x/12 + y/4 = P
and
w + z = 100

However, I am stumped at how to progress from here on. I tried playing around with the trigonometric functions in the triangle, but that seemed to complicate the problem even more. Does anyone has any insight into this?

 

[labyrinthus]

I'm still having trouble on figuring out what to do next >.<