Pow9

POW 9: Around the HornÐ'

Problem Statement

During the time of crossing the overland trail, many people instead chose to take the ship route which went around Cape Horn at the tip of South America. The points that we are given to keep in mind are:

-A ship leaves New York for San Francisco on the first of every month at noon, and vice versa for a ship coming from San Francisco.

-Each ship arrives exactly six months after it leaves.

With these things, we are also going to assume that:

-The weather conditions are perfect and the trip goes exactly as planned.

-The time zones do not affect anything in this problem.

-There is a certain point that the ship must reach, or have reached at each month.

Assuming these things, and having the given knowledge, we are to answer the question, if you were on a ship leaving from New York, how many ships from San Francisco would you see in passing?Ð'

Process

At first, I was confused with this problem and did not know what to do. For this problem, I used only one problem and it was what helped me solve it. With my table group (Derick & I), we did a simulation. We first drew out a large map with the points that every ship should reach at the start of every month. Then we kept feeding in the blocks (which we used to act as ships) and did the simulation. Using this strategy, we were able to find the solution.Ð'

Solution

I found that if I were a traveler on a New York ship bound for San Francisco, I would see SEVEN ships from San Francisco, California along the way. This is how I figure:Ð'

Starting: Both ships leave their starting points.

1st Month: Both ships arrive at their one month point. No ships have been seen.

2nd Month: Both ships arrive at their second month point. No ships to be seen.

3rd Month: Both ships arrive at their third month point, also their halfway point. The ships finally meet. One ship has been seen.

4th Month: Both ships arrive at their fourth month point. On the way there, our tracker ship (the first ship from New York) sees one ship coming from its (the New York ship) destination (5th month point) and heading to it's (the New York ship) previous point (the halfway point). And when the ship finally reaches the fourth month point, it stops and meets the ship from San Francisco that has stopped there. This counts as two ships that have been seen on this journey from third month point to fourth month point and makes a total of three ships seen so far.

5th Month: The same thing happens as the journey from third month