By: Eric Muhlenkamp and Nick “Ceps” Rose Gilligan’s Island By: Eric Muhlenkamp and Nick “Ceps” Rose http://www.popmodal.com/video/695/Gilligans-Island-Theme-Song

The Problem: Starting on a tropic port, 5 passengers set sail one day for a three hour tour. The weather started getting rather rough and the ship was tossed. If not for the courage of the fearless crew, the Minnow would be lost. With Gilligan, the skipper, the millionaire and his wife, the movie star, the professor and Mary Anne, the crew had a crucial decision. Trapped in the middle of the storm, Gilligan spots an island located 50 miles south and 30 miles west. Looking 50 miles south, Gilligan sees that there is calm water. The skipper tells the crew (Gilligan) that they can travel 30 mph in calm waters and 15 mph in rough waters.

The “Minnow” The island

Problem #1 The crew is trying to get to the island as fast as possible. How many miles should they travel in calm waters, and how many miles in rough waters? Justify your solution using the second derivative test.

30 mph in calm 15 mph in rough

Graph of Since the graph goes from negative to positive, it satisfies the second derivative test X intercept = 28.867513

Problem #2 How long does the fastest route take?

X= 28.867513 T= 3.39 Hours

Problem #3 A hurricane is traveling south towards the island at a constant rate of 15 mph, and is 60 miles directly north of the island. Will the minnow make it to the island before the hurricane hits? If so, determine the interval for x that represents the possible paths the crew could have taken to the island and still arrive safely if the distance traveled in calm water was 30-x.

Since the hurricane is traveling 15mph and Is 60 miles north of the island, it will get there in 4 hours. Sooo they need to get there in under 4 hours.

X=13 4.0108 X=14 3.9949 X can not be greater than 30 because of the equation