Finding the optimal path across two point with varying speed

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The discussion focuses on finding the optimal path between two points, A and C, with varying speeds along two segments, AB and BC. The user has established equations for time based on speed, but is unsure how to proceed with the problem. They attempted to incorporate trigonometric functions but found it complicated. The main challenge lies in optimizing the path to minimize travel time while adhering to the constraints of the problem. Further guidance is sought to clarify the next steps in solving this optimization issue.
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Homework Statement


[PLAIN]http://img214.imageshack.us/img214/194/calcdr.jpg
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?
 
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I'm still having trouble on figuring out what to do next >.<
 

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