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Solving a Work Application: Cleaning a House
Apply the problem-solving strategy for work applications to find how long it takes an individual to clean a house alone given the combined time. If Ra’shon can clean the house in hours alone, let be the number of hours his sister takes to clean it alone. In hour, Ra’shon completes of the job, and his sister completes of the job. Since it takes them hours working together, they complete of the job in hour. The rational equation is: Multiply both sides by the least common denominator, : 21s \left(\frac{1}{7} + \frac{1}{s} ight) = 21s \left(\frac{1}{3} ight) Distribute and simplify: Subtract from both sides: Divide by : Converting the improper fraction to a mixed number yields hours. Since of an hour is minutes, it would take Ra’shon’s sister hours and minutes to clean the house alone.
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Intermediate Algebra @ OpenStax
Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax
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Solving a Work Application: Cleaning a House
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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 commercial cleaning service is estimating job durations for a new contract. If a lead cleaner can complete a specific job in 7 hours and a trainee takes hours to complete the same job alone, they can finish it together in 3 hours. Which of the following rational equations correctly models this work application?
A residential cleaning company is training supervisors to estimate job durations. In a specific scenario, a lead cleaner takes 7 hours to sanitize a house alone, while an assistant takes hours. When they work together, the job is completed in 3 hours. Match each component of the work application to its corresponding mathematical term used to set up the problem-solving equation.
A commercial cleaning service is training supervisors to estimate project completion times. A lead technician takes hours to clean a standard facility alone, while an assistant takes hours. Working together, they finish the facility in hours. Arrange the following steps in the correct order to set up the rational equation needed to find the assistant's solo cleaning time.
A commercial cleaning service uses the rational equation rac{1}{7} + rac{1}{s} = rac{1}{3} to plan a project where a lead cleaner takes hours to finish alone and an assistant takes hours. True or False: In this equation, the term rac{1}{7} represents the portion of the facility the lead cleaner completes in hour.
Interpreting Labor Models in Facility Management