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Solving a Work Application: Finding an Individual's Painting Time
Apply the problem-solving strategy for work applications to find how long it takes an individual to paint a room alone. If Alice can paint the room in hours alone, let be the number of hours it takes Kristina to paint it alone. In hour, Alice paints of the room, and Kristina paints of the room. Since it takes them hours working together, their combined rate is of the room per hour. The rational equation is: Multiply both sides by the least common denominator, : 12t \left(\frac{1}{6} + \frac{1}{t} ight) = 12t \left(\frac{1}{4} ight) Distribute and simplify: Subtract from both sides: It would take Kristina hours to paint the room by herself.
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Intermediate Algebra @ OpenStax
Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax
Algebra
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Solving a Work Application: Weeding a Garden
A project manager at a manufacturing plant is evaluating the efficiency of two different assembly lines working together to fulfill a large order. To solve this 'work application' problem, arrange the steps of the standard problem-solving strategy in the correct chronological order from start to finish.
As an operations manager, you are setting up a work application to determine how long it will take two different data processing systems to audit a company's financial records simultaneously. According to the standard problem-solving strategy, what does the variable represent in the rational equation ?
In a professional environment—such as a logistics hub where multiple conveyor belts process packages—technicians use a specific problem-solving strategy to calculate efficiency. Match each component of the work application strategy with its correct definition or purpose.
In the standard problem-solving strategy for work applications—such as when an employee is assigned a specific task—if the individual takes hours to finish the job alone, then the part of the job completed in one hour is correctly represented by the expression .
Solving Equations in Logistical Work Applications
Learn After
A facility maintenance supervisor is estimating the labor needed to repaint an office suite. Marcus, an experienced painter, can finish the job in 7 hours alone. Sarah, a new assistant, would take hours to complete the job alone. When working together, they can finish the painting in 4 hours. Match each description of their work to the correct mathematical expression used to set up the problem.
A project manager is calculating the time needed for two employees to complete a task. If Employee A can complete the task alone in hours and Employee B can complete the task alone in hours, which equation correctly represents their combined work rate if they can finish the task together in hours?
A commercial painting contractor is estimating the time it will take for a new hire to complete a job alone. The contractor knows that they can finish the job in 6 hours alone, and that together they can finish it in 4 hours. Arrange the following steps in the correct order to solve for the new hire's individual painting time .
A facility maintenance supervisor is estimating the efficiency of a painting crew for a commercial renovation. If a professional painter requires hours to paint a suite of offices alone, the algebraic expression representing the portion of the suite they complete in exactly one hour is ____.
A facilities management team is calculating the time needed to paint a newly renovated conference room. If a senior painter can finish the room alone in 6 hours and an apprentice can finish it alone in hours, the equation used to model their combined effort to finish the room in 4 hours is .