Problem 36 - Introductory Algebra for College Students

Question

When two people work together to complete a job, describe one factor that can result in more or less time than the time given by the rational equations we have been using.

Step-by-Step Solution

Answer

One factor that can result in more or less time than initially calculated by rational equations is the variation in individual productivity levels over time due to elements such as fatigue or changing motivation levels.

Step 1: Understanding the Model

In tasks that involve multiple individuals working together, the time required to complete the task is often estimated using rational equations. These equations often assume that each individual's work output is uniform and independent of time or other individuals' output. Therefore, they can sometimes fail to capture the actual time it takes for the task to get completed in reality.

Step 2: Identifying a Factor

Many factors can affect the actual completion time. One of these is the variance in individual productivity levels. People work at different paces, and this can change throughout the day. If a person becomes fatigued or lacks motivation, their productivity could drop, leading to an increase in the time it takes to complete the task.

Step 3: Applying the Factor

For example, consider a task that, according to the rational equation, should take two people working in tandem 4 hours to complete. If one of them works at a slower pace than the other or their efficiency decreases halfway due to fatigue or diminished motivation, it could take longer than 4 hours for them to complete the task because the contribution of that person to the task completion becomes lesser than originally anticipated.