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A trail runner tries to run a hiking trail in record time. Consider a path through the mountains from x = A to x = B that is modelled by the function f(x). A B (a) (3 points) Assume first that the trail hiker runs a constant velocity U. Write down an expression for total time T that it takes the trail runner to run the path from x = A to x = B. (b) (7 points) Now let's try to model the velocity function more accurately. Suppose the velocity of the trail runner at any given point is given by: 255 mm) = W where S is the slope (inclination), h is the height (altitude), and d is the distance from the starting point. Using the slicing method in detail, find an expression for the total time T it takes the runner to complete the path from x = A to x = B