1. The problem statement, all variables and given/known data A hiker starting at point P wants to get to a forest cabin, which is two miles from the road at point Q (See diagram). The hiker can walk at 6.00 mph on the road and 2.50 mph through the forest. Suppose the hiker walks a distance X down the road before cutting through the forest, straight to the cabin. Determine the value of X for which the trip take the least time. Consider the distances to be good to three significant figures. 2. Relevant equations Trigonometry and Derivatives 3. The attempt at a solution I attempted to draw the lines again and label points to simplify the triangle. However, I am getting stuck on how to optimize the walk.