Math of "The Martian" Intro

I love the book "The Martian" mostly because unlike most entertainment these days where the hero succeeds through violence, in "The Martian" our hero succeeds through the use of math, science, and creative thinking. It such a great example of the kind of people who should be our role models, but sadly are all too often not.

I love the book so much that I am reading it for the fourth time now. But this time is different, this time, I am slowly going through, and pulling from the book as many math or science problems I can find that should be able to be solved by Junior High and High School level students.

Before we can get into the problems, I must paraphrase the first chapter of the book: 

(Note that because the length of a "day" is different on each planet, NASA uses day to refer to 24 hours, and Sol to refer to the length of a day on a given planet. Given that the story takes place on Mars, a Sol is 24 hours and 45 minutes.)

In the 2050's NASA put together the Ares missions, 5 missions to put humans on Mars. Each mission would be on the surface for roughly a month, and they would be spaced about 4 years apart. Mark Watney is the mission Botanist, and Mechanical Engineer on the 3rd Ares mission. 

On Sol 6 of their surface operations on Mars their camp is hit by a dust storm so powerful that the mission commander is forced to abort the mission early and return to earth. While the team is struggling through the dust storm to get to the rocket to leave, the main communication dish for their base camp breaks loose, it slams into the wires that make up the camp's secondary communication array. One of those wires breaks loose, hits Mark Watney and sends him flying into the storm. 

The wire doesn't kill Watney, but it does destroy the computer that relays his health data to the rest of the team, so to them it appears that he has been killed.

The remaining five members of the team try to search for him, but with visibility in the storm down to a few feet, no data coming in from Watney's health monitors, and the storm threatening to destroy the only rocket that can take them home, they are forced to leave.

On Sol 7 Mark Watney wakes to find he is alone on Mars. The next mission to Mars isn't due to touch down for 4 years, and it's slated to land almost 3200 kilometers from his camp. He has no way to contact the rest of his crew or earth, and he has supplies that were designed to last 6 people for two months...