Final answer:
To divide tasks efficiently, Bryan should focus on bush trimming, where he has a higher relative speed advantage, and Jim should focus on grass cutting, allowing both to work concurrently and maximize overall productivity in their lawn care business.
Step-by-step explanation:
To suggest how Jim and Bryan should divide their lawn care tasks of grass cutting and bush trimming, we need to consider their respective rates of completing the tasks. Jim can cut a 1/2 acre lawn in 3 hours and trim 8 bushes in the same amount of time, while Bryan can cut a similar lawn in 2 hours and trim 8 bushes in only 1 hour. By comparing these rates, it's clear that Bryan is faster at both tasks. However, since Bryan is relatively much faster at trimming bushes than Jim (trimming 8 bushes per hour compared to Jim's 2.67 bushes per hour), it would be more efficient to have Bryan focus on bush trimming while Jim focuses on grass cutting. This allows their lawn care business to maximize the number of tasks completed in the shortest time. Since grass cutting is a larger job in terms of time commitment, Jim can simultaneously start cutting grass, which allows both tasks to be done more efficiently when working together on the same property.