MAT 143 Project: Conquering Quantity – Raiders of Machu Picchu
Machu Picchu is a fifteenth-century Incan ruin located in the Andes near the Peruvian city of Cuzco. As one of the few well-preserved pre-Columbian ruins, Machu Picchu was named a UNESCO World Heritage Site in 1983. Today, Machu Picchu is one of the most visited tourist destinations in Peru; but it has only been widely known for about one-hundred years. Hiram Bingham, one of the earliest visitors to the site, is often credited as the scientific discoverer of the Machu Picchu. He returned to Yale University from several archaeological visits to the site with bones and other artifacts over which there is still on ongoing dispute between the Peruvian government and the university. Bingham is often cited as the inspiration for Indiana Jones, and like the fictional scientist, Bingham may be seen as more of a tomb raider than an archaeologist.
In this project, you will plan a vacation to Cuzco, Peru to hike the Inca Trail and visit Machu Picchu. You will do basic unit conversions using dimensional analysis, use estimation to allot your budget, and learn about Peru. Toward the end of the process, you will also consider what it means to be a responsible visitor rather than a raider of Machu Picchu. Grab your trusty fedora and army surplus bag and hit the road.
Day One: Fly to Cuzco, Peru.
Day Two: Enjoy Cuzco. Plan an activity in the city such as visiting a museum, shopping, or visiting a nearby archeological site.
Days Three through Six: Hike the Inca Trail and visit Machu Picchu.
Day Seven: Fly home.
To celebrate your college graduation, you plan to save $3000 to take a special vacation to Peru. In this part of the project, you will need to do some research to allocate funds for the different aspects of your trip. You will need to use a website such as Travelocity.com or expedia.com to estimate how much airfare will cost. You may use Travelocity, Expedia, or a travel guide from the library to estimate costs of staying in hotels or hostels, day trips around Cuzco, and the cost of hiking the Inca Trail. Travel guides can also help you decide how much you need to set aside for food and souvenirs. You might also take a look at the Explore By Yourself website: https://www.explorebyyourself.com/en/peru/ Once you have completed your research, fill in the Vacation Table and use it to total your costs. Remember, you only have an allowance of $3000, so plan wisely.
2. You will need to convert US dollars into Peruvian currency for use during your trip. You can use the site http://www.xe.com to answer questions (a) and (b).
(a) What is the currency used in Peru?
(b) What is the exchange rate between Peruvian currency and US dollars?
(c) Use dimensional analysis and your answer to part (b) to convert your US cash allowance into Peruvian currency.
3. Write your answers to the following questions in complete sentences. You will find www.timeanddate.com/worldclock/difference.html helpful.
(a) In which time zone is Cuzco, Peru located?
(b) Does Peru observe Daylight Savings Time?
(c) You are traveling in May. By how many hours does the time in Cuzco differ from North Carolina?
4. How long is the Inca Trail in kilometers? Given that 1 mile = 1.61 kilometers, how long is the Inca Trail in miles? Use dimensional analysis and show your work.
5. The first day of the hike, you cover 12 kilometers in 6 hours. What was your average walking speed in miles per hour? Use dimensional analysis and show your work.
6. Using the average walking speed and the length of the Inca Trail calculated in the previous problems, how long should it take you to walk to Machu Picchu? Use dimensional analysis and show your work.
7. What is the highest peak in North Carolina? How tall is it in feet? Write your answer in a complete sentence.
8. How tall, in meters, is the highest peak on the Inca Trail? Write your answer in a complete sentence.
9. Given 1 foot = 0.30 meters, use dimensional analysis to convert the height of the tallest peak on the Inca Trail to feet. Show your work.
10. Suppose you are taking your vacation in May. What is the average daytime temperature in degrees Celsius on the Inca Trail during that month?
11. Peru measures temperatures in the Celsius scale, while the United States records temperatures in degrees Fahrenheit. Convert the average temperature on the Inca Trail into degrees Fahrenheit given that F= 9/5 C+32.
12. How does the temperature in North Carolina compare with the temperature in Cuzco, Peru during May?
13. During your journey, you develop an abscessed tooth and have to visit the dentist. You are prescribed an antibiotic with a dosage of 7.5 mg/kg every six hours. If you weigh 120 pounds and the antibiotic comes in 250 mg tablets, how many tablets should you take each day? Use dimensional analysis and show your work.
14. If you need to take the pills for five days, how many tablets should the pharmacist give you when she fills your prescription?
Many places like Machu Picchu where no-one lives have large numbers of visitors. Those people affect the place they are visiting, and the more of them there are, the greater the effects of their presence will be. In the next several questions, we’ll examine just how many people visit Machu Picchu each day, consider their effect on the site, and contemplate how to be responsible visitors rather than raiders.
15. Machu Picchu currently has about 18000 visitors daily. The area of Machu Picchu is about 13 km2. Calculate the daily visitor density, or how crowded Machu Picchu is, in daily visitors per square mile. Use dimensional analysis and show your work.
16. Carrboro is the most densely populated town in North Carolina. Go to ZipAtlas http://zipatlas.com/us/nc/city-comparison/population-density.htm and look up the population density of Carrboro in people per square mile. How does this compare with the daily visitor density you calculated for Machu Picchu? Write your answer in complete sentences.
17. The many visitors to Machu Picchu are affecting the environment and people who live near the site. What is being done to help protect Machu Picchu? What is being done to help the people who live in the nearby towns? How can you be a responsible traveler during your visit? Read the following articles and write a paragraph to answer these questions.
Can We Protect Machu Picchu? (n.d.). Retrieved March 27, 2015, from http://www.ethicaltraveler.org/2011/10/can-we-protect-machu-picchu/
Saving Machu Picchu (n.d.). Retrieved June 28, 2020 from https://www.smithsonianmag.com/travel/saving-machu-picchu-153497816
MAT 143 Project: Conquering Quantity – Raiders of Machu Picchu