DUNCAN'S POW #4 - Room 105

The Problem

Last week, Mr. Sala went on a journey in which he touched every single continent. This week we must figure out why some classmates got longer or shorter routes than I did.

I think the possible differences fall into three main categories: 1) Path differences; 2) Arithmetic errors; and 3) Map errors.

Path Differences

Different students may have chosen different paths for Mr. Sala to follow. I think I saved miles by using the canals that pass between continents.

Arithmetic Errors

It is possible that in converting from measurements on the map to actual miles that someone might make an error.

There are lots of ways to make mistakes calculating the time Mr. Sala would take. My mom divided the number of hours it would take Mr. Sala by 24 hours per day and then tried to add 6 hours sleeping time back in. It got very complicated, and she got a different answer than I did. I just divided the total number of hours Mr. Sala would spend kayaking by 18 hours of kayaking per day to get the number of days. My method was simpler.

Map Errors

As I explained last week, all maps are less accurate than a globe for this problem.

Different map projections also will give different answers. Also, particularly with cylindrical projections like the Robinson or Mercator projections, the scale of the map can vary by latitude. For example, I checked a Robinson projection map that says the scale is one inch = 523 miles, but that is only the correct scale at 38 degrees latitude. At 0 degrees latitude, the equator, one inch equals 600 miles. At 90 degrees on the map, one inch equals 190 miles.

If someone ignored these difference in the scale, they could get an answer that is very wrong. For example, the same trip could appear a lot longer or a lot shorter, according to which part of the scale they used, even if a person used the exact same path and map.

Leg Of Trip  Distance Using 1"=190 miles  Distance Using 1"=600 miles  Actual Distance (From Globe) 
N. Amer. to S. Amer.  0 0  0
S. Amer. to Europe  1770 5400  4798
Europe to Africa 760 2400   2525
Africa to Asia 0 0  0
Asia to Australia  1770 5400  7070
Australia to Antar.  950 3000  2525
TOTAL DISTANCE  5,250 21,450  16,918

The comparison came out the way we thought it would. Depending on the scale, one person could find a distance that was about three times longer than another, even with the same path.