By: Eric Muhlenkamp

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Gilligans Island

• By Eric Muhlenkamp
• and Nick Ceps Rose

http//www.popmodal.com/video/695/Gilligans-Island
-Theme-Song
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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.

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The Minnow
The island
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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.

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30 mph in calm
15 mph in rough
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Graph of
Since the graph goes from negative to positive,
it satisfies the second derivative test
X intercept 28.867513
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Problem 2

• How long does the fastest route take?

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X 28.867513
T 3.39 Hours
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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.

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• 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.
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X13 4.0108 X14
3.9949 X can not be greater than
30 because of the equation