Work Rate. The time T required to do a job varies inversely...

Work Rate. The time $T$ required to do a job varies inversely as the number of people $P$ working. It takes 5 hr for 7 bricklayers to build a park wall. How long will it take 10 bricklayers to complete the job?

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Key Concepts

Constant Work Principle

The constant work principle is the concept that the total amount of work remains fixed, regardless of the number of people working on it. This principle allows one to set up equations that express the relationship between workers and time by ensuring the product of the number of workers and time remains unchanged.

Inverse Variation

Inverse variation describes a relationship where one quantity increases as the other decreases in such a way that their product remains constant. In work rate problems, when the number of workers increases, the time required to complete the job decreases proportionally, assuming constant efficiency.

Work Rate

Work rate involves understanding how quickly a task can be completed, typically by considering the amount of work done per unit time. In these problems, the total work is constant, and the work rate is determined by multiplying the number of workers by the individual work rate of each worker.

Proportional Reasoning

Proportional reasoning is a fundamental mathematical skill used to compare the ratios between quantities. In the context of work rate problems, it assists in determining how changes in one variable, such as the number of workers, affect another variable, like the time required for completion.

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