How far do I travel, how far do I go? 

 

                                                           
               
(Welcome, Mrs. Yount's Pre-Calculus students. Read the introduction and the task, then use the links under number three to do the problem. You may choose one of the cities to complete the assignment for extra credit. Due Monday, March 6. Remember you must find a direct flight!!! Good Luck!!!)

1. Introduction: You are curious about airlines charging you for how far you fly, but not how far you really travel. They charge you for the miles you go when you fly, but how far away are you really? In other words, when you fly around the earth, you fly the path of an arc, but distance is measured on a straight line. Should the price change, and are you being charged too much? You have four destinations in mind to reach from New York's JFK airport: Los Angeles, CA; Cairo, Egypt; Istanbul, Turkey; and London, England. You need to find direct flights to these destinations and find out how far it is. You also need to look for the cheapest price.

2. Task: First, you need to find the distance and price for each flight. You may want to use a map to find each of these cities on the earth, though it is not necessary. Then you need to draw a 2-dimensional representation of each flight around the earth. Label your drawing with the information you found. Now, using your mathematical genius, find the distance you actually travelled. (What other information do you need to know? What formulas will you use to help?)

3. Sources:

http://edit.yahoo.com/config/ytravel?resform=YahooFlightsR

http://www.sisweb.com/math/tables.htm

The earth's diameter is 7269.4 mi.

4. Process: Once you have your data, and have done your calculations, do the following:

a. Find the cost per mile the airline charges you. Next determine the price the flight would cost if you were charged per actual mile travelled. How much more are you paying? Calculate this difference as a percentage.

b. Make the following prediction: For each flight, find the ratio of miles you fly to actual miles travelled. Will this ratio be the same for each flight, or will it vary? Why or why not? Pair several flights to check your prediction. If the ratio is the same, what is it?

c. Make a line graph in Excel that has as the x-axis the actual distance, and the y-axis the flown distance. Find the equation of the best-fit line. Make a bar graph for each destination showing the difference in the actual price and your predicted price.

d. Using Word, write a brief summary to explain your findings. Paste your graph from Excel into the bottom of your summary.

e. Make a PowerPoint presentation with a title page, a slide for each 2-D sketch with labels, and your line graph, which you will present to class.

5. Conclusion: You have used actual real-world data to solve a very complex problem. And you saw how useful math can be, and how neatly it can be displayed and presented using technology.