Suppose that you are traveling west with a load of fine silk. At Dunhuang, your caravan guide informs you that you must pack at least 8 liters of water per day for the trip across the desert. Your camel can carry an additional 70 kilograms. Will you have to get an additional camel to transport the needed water? Explain your answer.
After carefully listening to stories from older merchants you have determined that the value of fine silk increases by 50% for each 1000 miles it is moved to the west. Further you determine that fine rugs from Baghdad increase the same amount for each 1000 miles they are transported to the east. You determine to make the trip from Chang’an to Baghdad with a load of silk. After arriving in Baghdad you plan to trade the silk for Persian rugs, which you will sell back in China. If you leave with $1000 worth of silk, what value should you have upon trading in Baghdad?
[ Hint: use the miles between cities figured earlier (about 6000 miles).]
A rival merchant from Chang’an also has plans to trade silk for Persian rugs, but the rival is only going as far as Kashgar. There the rival will sell the silk and buy the rugs for later sale in Chang’an. The rival will not make as much money, but believes that he can make two such trips while you make only one. If the rival actually can make the two trips to your longer one, who will have the greater profit from the business (assume the expenses of caravan travel are the same for your one trip and for the rival’s two trips)?
Changes Over Time
Students often fail to realize that cities may change names over time, depending on various historical actions such as war and occupation by other countries. Exploring such changes provides another opportunity to integrate mathematics and social studies, along with technology through exploration via reference books or the Internet.
For the next exercise students investigate which cities mentioned in the Silk Route have had name changes since 700 AD. For example, Byzantium changed to Constantinople and is now Istanbul. However, Damascus, Baghdad, Tyre and Dunhung are still called by the same names. What kind of reference book could be investigated to check on city names?
Using a current map, plot a route that passes through the cities mentioned in the story from Chang’an (now Xi’an) to Tyre. Then approximate how long it would take to travel that route by truck if the driver actually drives for 10 hours per day and can average 50 miles per hour (assume that there are no problems passing from one country to another). (Answer: 12 days) How much would it cost if you hire a truck driver at a rate of 55 cents per mile? The driver pays for the fuel at a rate of 75 cents per liter. If the truck can average 8 miles per liter of fuel how much will the driver make for the entire trip?
If the truck driver had to have his/her passport stamped at each border crossing how many times would the truck driver have had his/her passport stamped?
Conclusion The ideas discussed here are just a few of the ideas that tie mathematics with a story of early commerce between two major civilizations, Chinese and Persian of the late first millennium, that are not often featured in the social studies curriculum. The focus here was on mathematical tasks. The Silk Route offers a treasure of other possible activities and investigations.