Solve the variation problems in Exercises 93

Name: Problem 97, Chapter 3: Precalculus
Uploaded: 2020-05-07T21:02:13-08:00
Duration: 1 min 19 s
Channel: Charles Carter
Description: Solve the variation problems in Exercises 93–98. The time required to assemble computers varies directly as the number of computers assembled and inversely as the number of workers. If 30 computers can be assembled by 6 workers in 10 hours, how long would it take 5 workers to assemble 40 computers?

Solve the variation problems in Exercises 93–98. The time required to assemble computers varies directly as the number of computers assembled and inversely as the number of workers. If 30 computers can be assembled by 6 workers in 10 hours, how long would it take 5 workers to assemble 40 computers?

Solve the variation problems in Exercises 93–98.
The time required to assemble computers varies directly as the number of computers assembled and inversely as the number of workers. If 30 computers can be assembled by 6 workers in 10 hours, how long would it take 5 workers to assemble 40 computers?

Key Concepts

Combined Variation

Combined variation involves a situation where a variable is simultaneously directly proportional to one factor and inversely proportional to another. By integrating both types of variation into a single equation, one can model complex scenarios where multiple factors affect the outcome, ensuring a complete understanding of how these differing influences interact.

Constant of Proportionality

The constant of proportionality is the fixed factor that relates two variables in both direct and inverse variation. It allows us to create an equation that models the relationship between the quantities. In combined variation problems, this constant is determined using known values, and it facilitates the prediction of new outcomes under different conditions.

Inverse Variation

Inverse variation describes a relationship where one quantity increases as the other decreases, such that their product remains constant. This is used in scenarios where a quantity, such as time, is inversely proportional to another factor such as the number of workers. Understanding inverse variation is crucial for determining how changes in one variable affect another in a non-linear way.

Direct Variation

Direct variation describes a relationship between two quantities in which an increase in one quantity results in a proportional increase in the other. In problems involving direct variation, the ratio between the two quantities remains constant. This concept is essential when a quantity, such as time or cost, is directly proportional to another factor like the number of items produced.

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