Final answer:
Assign dishwashing to yourself as you are significantly faster at it, and vacuuming to your roommates to optimize total cleaning time, while being mindful of potential issues related to efficiency imbalances.
Step-by-step explanation:
Optimizing Roommate Cleaning Duties for Maximum Free Time
If you have recently moved to Washington, D.C. and find yourself quicker at cleaning tasks than your roommates, strategic delegation can maximize your free time. Given that you are 70% faster at dishes and 10% faster at vacuuming, you should assign the task you are least relatively quicker at to your roommates. In this case, you should take on the dishes, while your roommates handle vacuuming, to get the most out of the shared cleaning time. This allocation ensures that overall cleaning is completed in the shortest possible combined time.
However, this imbalance in cleaning efficiency could lead to potential problems. These might include resentment if roommates feel they are assigned more burdensome tasks, or a lack of incentive for them to improve their own cleaning efficiency. To illustrate with a trade-related analogy, this scenario is akin to the principle of comparative advantage where each party should engage in the activity where they hold a relative efficiency, even if one party is absolutely better at both tasks.