About 20 years ago, a mathematician noted that his dog, when retrieving a frisbee in a lake, would run parallel to the shore for quite some distance, and then jump into the water and
swim straight for the frisbee. She would not enter the lake immediately, nor would she wait until she was on
the point on the shore closest to the frisbee. Pennings theorized that the dog entered the water at the point
that would minimize the total length of time it takes to reach the frisbee. Suppose that the dog runs at 13
mph along the shore of the lake but swims at only 4.3 mph in the water. Further, suppose that the frisbee is
in the water 60 feet off shore and 220 feet down the shoreline from the dog. Suppose that the dog enters the
water after running x feet down the shoreline and then enters the water. Compute the total length of time, T,
it will take for the dog to reach the frisbee. Next, determine a natural closed interval that limits reasonable
values of x. Finally, find the value of x that will minimize the time, T, that it takes for the dog to retrieve the
frisbee.