Final answer:
Assign yourself the dishes for maximum efficiency due to your 70% faster speed, and give the vacuuming task to your roommates. Be aware of potential fairness concerns. This scenario is analogous to countries specializing in goods they produce most efficiently.
Step-by-step explanation:
You just got a job in Washington, D.C. and moved into an apartment with roommates who do not clean up after themselves. Since you can clean 70% faster at dishes and 10% faster with vacuuming, the most efficient way to divide tasks is to assign yourself the job of doing the dishes daily, where you have the largest comparative advantage. Your roommates should take on vacuuming and possibly other cleaning duties where the time difference is less pronounced. This ensures the household chores are completed in the shortest combined time, maximizing overall free time for everyone.
However, this arrangement may lead to potential problems such as resentment from roommates who may perceive the division of labor as unfair. A trade-related analogy would be a situation where different countries specialize in producing goods and services that they can produce more efficiently than others, which is the concept of comparative advantage in international trade.