You can run at a speed of 4 mph and swim at a speed of 2 mph and are located on the shore, 3 miles east of an island that is 1 mile north of the shoreline. How far (in mi) should you run west to minimize the time needed to reach the island?

Answer 1

If you run west for x miles, then you have to swim √((3-x)^2+1) miles
So, you want to minimize the total time, which is thus

x/4 + √((3-x)^2+1)/2