A Math Problem

We recently had our friend Bob Rebitzer and his daughters Elana and Maya visit us over New Year’s week while we were in Huatulco.  Elana had a school assignment/competition that she needed to complete which required her to interview someone to see how they use complex math in their everyday job.  It turns out that she wanted to interview me!  She just informed us that her write up won first prize in her math class for most interesting use of math on the job!  Her teacher read it aloud while adding imaginary details about fending off sharks!  She agreed to share her write up which follows below.

Michael Mitgang and his family live on a boat. Every day, they use high level math, sometimes in order to save their lives. This happened a few weeks ago, as they were crossing from Mazatlan, Mexico, to Huatulco, Mexico. Michael was worried about how much fuel they had left and the reader was not giving accurate readings. If they ran out of fuel, they would either start drifting, which could get them miles off track, or have to sail the rest of the way, which would slow down the speed of the boat. That could have made the journey much longer than they were prepared for.

Michael checked the engine hours on both the port and starboard engines, which tell you how far they have traveled (like an odometer on a car). He also measured the amount of fuel left with a dowel and ruler, by dipping into the tank. Using that, and a few other pieces of information, he was left with these categories for a table.

Port Engine Hours

Star Engine Hours

Change in hours since last meas-urement.

Inches of fuel left in tank

Change in Inches

Avg. RPM

Hours per inch

Est. # of hours left in tank

Avg. Speed

Amount of miles of fuel left

By filling in this table, Michael used algebra when he found the amount of miles of fuel left (X hours times Y speed equals miles of fuel left). Using that method, Michael could tell whether or not they had enough fuel left in the tank.

However, there was another problem.



The tank was shaped like this, so there were two categories of inches. The first was the amount of gallons of fuel per inch used when draining from only the taller cube. The second was the amount of gallons used when draining from both cubes. The difference between the two inches was substantial, greater than two full gallons per inch, so it turned out to be important to know the different drainage rates between the two types of inches. To solve this problem, Michael had to use geometry, while finding the total amount of gallons.

As a further problem, Michael and his family had no internet access at the time, and they didn’t know how many cubic inches were in a gallon. To find the amount of square inches in a gallon, Michael had to first convert inches to centimeters and gallons to liters (because he knew how many cubic centimeters were in a milliliter), and then convert back into gallons.

Every day, the Mitgang-Gottesman family faces similarly important problems, many of which having to do with high level math.

Michael, Anchored in Acapulco