Final answer:
Assign the vacuuming task to your roommates to make use of your comparative advantage in doing dishes more quickly, which allows for more free time. Ensure communication to prevent conflicts over chore division.
Step-by-step explanation:
When tidying up a resident's room, it is important to strike a balance between efficiency and division of labor. Given that you are 70% faster at dishes and 10% faster with vacuuming, you should assign your roommates to vacuum, since the difference in speed is less pronounced, granting them the sense of participation and reducing the likelihood of conflicts that may arise due to perceived imbalance of chores. Furthermore, doing so will maximize your free time because the time saved on dishes is significantly greater than that on vacuuming. This situation has a trade-related analogy to comparative advantage, where each party specializes in tasks they are relatively more proficient at, thus improving overall productivity.
However, there may be some problems such as reduced teamwork, feelings of unfairness, or lack of skill development in slower tasks for the faster individual. To avoid these issues, it is essential to maintain communication with your roommates and come to a consensus on the allocation of chores.