An electrician charges 45 per hour for her time and 24 per...

An electrician charges $\$ 45$ per hour for her time and $\$ 24$ per hour for her assistant's time. On a certain job the assistant worked alone for 4 hours preparing the site, and then the electrician and her assistant completed the job together. If the total labor bill for the job was $\$ 464,$ how many hours did the electrician work?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Aggregation of Costs

This concept refers to combining various cost components—such as fixed independent charges and variable charges based on time—to determine the total cost. It requires summing the individual contributions to the total, such as additional hours worked by both the electrician and the assistant.

Linear Equations

The problem is solved by forming and solving a linear equation. Linear equations are fundamental in algebra and are used to model and solve situations where there is a constant rate of change. They allow the combination of different cost factors, like fixed preparation time and variable work time, into a single, solvable equation.

Algebraic Modeling

This concept involves translating a word problem into an algebraic equation by defining variables to represent unknown quantities and expressing relationships in terms of those variables. In time and cost problems, it means setting up an equation that accurately represents the total cost in terms of the hourly rates and hours worked.

Unit Rates

Understanding unit rates is crucial, as they show the cost per unit of time or labor. In problems like this, knowing the hourly charge allows us to relate the time worked to the overall cost, making it possible to convert minutes of work into money spent.

Transcript

Please give Ace some feedback