Calculating the quickest path between two points. Determine the pattern according to the situation, the quickest route from checpoint 1 checkpoint to 2 when the orienteer's running speed on the stomping is 2.5 times as large as on the swamp. X=750m and Y=400m

 A: Hint: Pythagorean Theorem
Let $h$ denote the distance of the hypotenuse (from checkpoint 1 to checkpoint 2, through the swamp), where the legs are measured as horizontal distance (x) and vertical distance (y). 
$$h^2 = (400)^2 + (750)^2 \implies h = \sqrt{ 400^2 + 750^2} =850\text{m}\,\text{through the swamp}$$
The alternative route to consider would be $400$ meters through the swamp (vertically), plus $750$ meters running on the stomping (horizontally). 
Now, compare the two routes given the differences in running speed on stomping vs. on swamp.
A: Hint:
Lets assume you run in a straight line to a point $x$ from point 2 along the stomping path. Then run along the stomping path.  How far do you travel and how long does it take.
Now from Pythagoras 
Distance travelled in swamp is:
$$ \sqrt{ (750 - x)^2 + 400^2} $$
Distance travelled alond stomping path is:
$$ x $$
Now we don't know absolute speed but we know relative speed so time for the journey is proportional to.
$$ x + 2.5 \cdot \sqrt{ (750 - x)^2 + 400^2}$$
Your task is to find $x$ to minimise this time.  What do you know about the derivative of a function at a maximum or minimum? 
