Chapter 4: Salvaging

They had survived!

Justin was soggy and cold, but at least he was alive and unhurt. So were his mother and the other passengers from the sailboat. The previous night’s storm had thrown their sail boat against a rocky outcropping just off shore. They managed to scramble ashore as the winds and rain abated.

The captain and her teenage nephew were scouting the beach for useful debris from their shipwreck. Random bags and boxes had floated onshore near them. The boat lay in ruins on the rocks. It finally struck Justin that they were shipwrecked for real. Three weeks earlier Justin had begun planning for the start of his 8^th grade year. Then, out of the blue, his mother told him that they were going on a chartered Caribbean sailing trip with people he didn’t know. While on this trip, a storm overtook the ship. And now here he was, stranded with his shipmates. It felt like some bad t.v. movie plot.

Justin’s mother held onto him silently. Jesse, the weather guy, stood up to help the captain. The three college students, a guy and two women, sat huddled against a stone. Justin could hear the captain speaking with her nephew and Jesse, but the rest of them just stayed silent.

The Captain, her nephew and Jesse came towards them with several sacks salvaged from the ship. 

“Look” she said, “we have to accept the fact that we’re stuck here on this island until we can figure a way get off. Jake, Jesse and I were talking and we think we should explore this place. An island this big has to be inhabited by people somewhere. There must be some sort of town or something over in that direction.”  She pointed up over the red clay cliffs to the green mountains. “We’ll split up into two groups: Jake, Justin and Cynthia will go with me with up the beach and out over that pass in the distance. Jesse, Jeanie, Marge and Miguel: you guys will head up over there, “she pointed to what looked like a crack in the cliffs that formed a sort of pathway up into the mountains. Justin saw Miguel get all serious, even a little bothered, by what the captain said, but kept quiet.

The Captain and Jesse both emptied out the sacks they had carried over to the group. Out fell rope, food packages, canteens and random other items they had deemed useful. Jesse took up one of the empty sacks and said, “These sacks can be fashioned into a sort of backpack. We’ll split up these items between the two groups. We figure that when one of the groups finds civilization, it can send out one of these flares.” He held one up to show them. 

“This is getting more like a silly t.v. show every minute,” Miguel muttered. Jesse ignored the comment and continued. Everyone else started to divvy up the stuff between the two sacks. Jesse approached Justin with two large canteens and a cup. 

“Hey Justin, I have this task for you. In this first canteen I emptied a liter bottle of water. In this other is a liter of Gatorade. Both of the bottles were starting to break.  We want to split the liquids up evenly between the two groups but we only have these two canteens to carry them. We’ll have to mix every thing up.”

“How will we know he’ll do it fairly,” interrupted Miguel with some severity. Justin grew a little nervous at Miguel’s apparent mistrust of him.

“That’s easy,” replied Jesse. “All you have to do, Justin, is pour out a cup of this Gatorade, mix it into the water canteen, then pour out a cup of that mix and put it back into the original Gatorade canteen. Both canteens will have not only the same amount of liquid, but also the same concentration.”

Your task: Is Jesse correct? If this is true, does this method work for any volume. If false, is there a better way to do this with the materials available to them?

Chapter 3: Sailing

Five days into the sailing trip Jesse was having serious regrets. What had begun as unbearably exciting had become torture. Barely an hour after setting out to sea, his normally baritone voice went quiet and he sat pale faced in one corner of the boat. He felt fuzzy headed and nauseous.  After two hours, he started vomiting. The captain and her assistant initially laughed off the incident as one more passenger working to earn his sea legs. To his chagrin, nobody else showed any sign of sea-sickness. Even after his stomach calmed down, his head continued to pound. Jesse decided that laying down in his bunk was his only option. He basically stayed there for entire days at a time, only venturing out when they made landfall at some island.  

It wasn’t supposed to be this way. He had just accepted his first real job as a meteorologist for the local television station. It occurred to him to book this sailing cruise to celebrate his new career move as well as to acquire some important real world weather experience that he was lacking after living in academia for so long. The wrenching lurches and lunges of this boat quickly took away both the celebration and the real weather experience.

Jesse knew that September was a very interesting time in the Caribbean. The weather was balmy but fresh breezes hinted at changes to come. The ocean was water was its warmest temperature of the year.

The Captain stopped laughing off Jesse’s illness. She was serious when she brought Jesse water and some Dramamine. She insisted he come above board and take the helm of the ship as they sailed.  She told him to set his sight on the horizon as a way to combat the nausea and headaches. She set off to work on the sails. 

He looked out over the horizon. It was no longer the light blue contrasting the deeper hue of open sea. Dark clouds were gathering quickly. The breeze turned into a wind and the sea grew choppy. The Captain and her nephew started tying down equipment, tightening the sail and telling the other passengers to go inside.  Jesse knew that some serious weather was coming their way and he cursed himself for not looking into it more seriously before booking this trip. If anybody on this ship could predict the weather, it should be him.

The captain came hurriedly towards Jesse, wet from the waves crashing in on them from all directions. 

“We’re in trouble. We need to send out an SOS to any ships nearby. Go down in the cabin to the radio. You should also check the radar to see if there are any land masses close by. Move it!”

Jesse scrambled down the hatch. Sea sickness had been replaced with dread.

Your task:

Radars are radio wave sent from a radar station and reflected by the target to the station, causing a spike to appear on the wavy line. The indicator is marked so that the number under the spike shows the distance in miles from the station to the target. The left screen supplies data from the shore radar station at A, the right screen from B. How can you use the 75 and 90 numbers on the indicators to locate a target? Exactly where is the target on an extension of this map? Draw this map. What assumptions did you need to make to solve this problem.

Chapter 2: Loading

Patricia sat on the edge of the sailboat watching a group of people walking slowly down the dock with their baggage in tow. This was going to be the last sailing trip she would captain for a long time. After this two-week trip around the Caribbean, she would be handing over the keys to the boat’s new owners and setting off to her new life. If only she knew what that was.

Even after 10 years guiding one group of vacationers after another between the islands, she had not lost the sense of excitement before each trip. What awaited them just over the horizon was both known and mysterious. She was sure she had visited every island and rocky outpost between the Puerto Rico and the Mexican coast.  But deep down she knew that the ocean was far deeper and secretive than it let on to the casual observer.

This summer had treated her well. Her trips had been booked earlier than normal and her clients had been a cut above the rest in terms of their competency and sense of adventure. In addition, she had developed a very close relationship with her 17 year-old nephew. When her sister had called her last spring and suggested that she offer Jake a summer job on her boat, Patricia initially balked. She hardly knew her nephew and he had never spent time on a boat. But her sister needed this favor and so she relinquished. To her surprise, Jake was a quick student and enthusiastically took on the responsibilities of ensign. Soon she wondered how she had ever sailed without him.

“Aunt Patty, I finished putting away the supplies.” Jake sat down next to her to watch the six passengers struggle down towards them. “Should I go help them?” he asked. Patricia nodded negatively. She had long ago learned that for these trips to be successful, the passengers had to understand they would be responsible for their own stuff. But why did they always bring so much?

They approached the boat. Patricia and Jake stood up and waved to them with huge smiles on their faces. Patricia recognized the mother and her son as they came forth first. She was very impressed with the tiny suitcases each had in their hands. 

“Hi, you must be Cynthia and Justin. Welcome to the S.S. Gobio.” She shook their hands just as the other four passengers approached. 

A tall man in his late twenties spoke out in a boomingly cheerful voice “I’m Jesse, you must be the captain?” Patricia nodded. He looked around the boat.

“Pretty cool. Even looks better than it did on your website”. 

Behind Jesse were two women and a man in their early twenties. They introduced themselves as Jeanie, Michelle and Miguel. They had signed up for this trip as one last summer adventure before returning back to their senior year at college. 

Just before Patricia was going to launch into her explanation of rules and regulations of her boat, Jesse raised his hand and said:

“You know what, guys, look over there.” He pointed to the numbers on the ship: 45254. “ You know what that kind of number that is? Palindromic. It reads the same backward as forward. The weird thing is that I noticed the same kind of number on our shuttle bus. When we got on, the odometer showed 15,951. At the time I thought it was strange and was sure that it would be a long time before that happened again. But almost exactly two hours later, when we arrived here, the odometer showed a new palindromic number.” 

Jesse looked at Justin and said, “What could be cooler than that?” Justin could think a several cooler things, but decided to keep quiet.

Your task: Based on the information provided, how fast was the shuttle traveling in those 2 hours?

Chapter 1: Packing

“Awesome!”


That was Justin’s first reaction when his mother told him back in July that he was going to miss the first two weeks of school to go with her on a Caribbean sailing trip she had booked a month earlier. But now he wasn’t quite so psyched. He felt left out from his soccer team and his friends as they chatted about their up-coming 8th grade year. He wondered what he would do without his cell phone or his laptop. He also wondered what was on his mother’s mind? It was so unlike her to disregard school and send him on such an adventure.


He wanted to go, to be sure. But why now and why with her? Did he have any choice about this trip? He sensed he couldn’t broach the subject with his mother judging by the distracted way she had sent him to his room to pack for the trip. He was both excited and confused at the same time.


In his room Justin reached under his bed and pulled the small suitcase his father had bought. He heard his mother’s cell phone ring and her muffled voice from down the hallway as she must have slipped into the kitchen. He heard her laugh. Who had called?


He was rummaging around his room when his mother called from down the hall.
“Justin, remember to pack enough clothes for the whole two weeks… I won’t be washing anything, ok?”


For many other kids his age this might have seemed like an easy task. But Justin was very particular about his clothing choices. He never wore the same clothes two days in a row, and he always washed his clothes after wearing them for a day. He also never wore a shirt that was the same color as his pants.


This presented him with a serious dilemma, one his mother wasn’t about to deal with in her current state. What to pack? To make matters worse, he was supposed to fit all his clothes, toiletries and a reading book into this tiny suitcase that only measured 24” by 24” by 12”. His father was gone on one of his business trips, his mother was mysteriously preoccupied and he here he sat on his bed frozen by his packing conundrum.

Your task: Create a practical packing plan for Justin. Determine what the reasonable number shirts and pants (or shorts) he needs to guarantee he can follow his clothing routine even on the sailing trip. You will also have to determine if all the clothes, toiletries and book will actually fit into the suitcase he has to use. Assume that his socks and underwear will use up about ½ cubic feet of his suitcase.  Create a detailed and organized list of the clothing items as well as a clear diagram (with dimensions) of how it will all fit in this suitcase.

Verdania: A Mathematical Odyssey

Think of Gilligan's Island being morphed in Lost, Myst or Ecotopia.

This Blog: Verdania: A Mathematical Odyssey, will follow the adventures of 7 shipwrecked people as they explore and come to know Verdania, the lost island in the middle of the Atlantic.

Along the way will be a series of mathematical problems that help flesh out the story as well as create new understandings.