DUNCAN'S POW #3 - Room 105

The Problem

Mr. Sala is ocean kayaking from one continent to another. He wants to touch the shore of every continent. We must determine the shortest route in which to touch every single continent. If he rests for 6-8 hours per day and can paddle at 10 miles per hour, we also must figure out how long it will take him.

How I Chose Mr. Sala's Path

I had Mr. Sala start in the middle of the Panama Canal. That way he could be in North America and South America at the same time. That's the same reason I had him go through the Suez Canal. I chose this path for Mr. Sala's kayak trip:

I Measured the Length of Mr. Sala's Trip Using A Globe

Why I Used A Globe Instead of A Map

The Earth is a sphere, so if you use a flat piece of paper some continents and oceans will not be the right sizes and shapes. For example, if you use a cylindrical projection, like a Mercator projection, only places on the equator will be the right shape and size. (The map above is a modified cylindrical projection.) If you use an azimuthal projection, only one point in the center is accurate. (I used an azimuthal projection to measure the "Distance On Map" below).

In this problem, if you use a map, you can get all your distances goofed up, because the size and shape of the continents and oceans will be incorrect most of the time. This means the distance of Mr. Sala's trip will be wrong.

Comparing The Globe Measurement To A Map

Here are my measurements for Mr. Sala's trip, using a globe and a map:

 Leg Of Trip Distance On Map (miles) Distance On Globe (miles) N. Amer. to S. Amer. 0 0 S. Amer. to Europe 4973 4798 Europe to Africa 2210 2525 Africa to Asia 0 0 Asia to Australia 6630 7070 Australia to Antar. 3315 2525 TOTAL DISTANCE 17,128 16,918
We proved our theory that using a globe you will get a different distance. The difference between the globe and the map we used is about 200 miles. It will probably be different, if we used different maps, too. This is because certain kinds of maps have accuracy for different areas and problems.

How Long It Will Take

To figure out how long it will take, we will multiply it by 1 hour divided by 10 miles (because that's his rate). That will give us the total number of hours he must travel. Then take the total number of hours times 1 kayaking day divided by 18 hours (that's the number of hours he kayaks each day). So, to cover the distance shown on the map, it will take Mr. Sala a little over 95 days. To cover the distance shown by the globe, it will take Mr. Sala exactly 94 days.