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Solving a Work Application: Painting a Room
Apply the problem-solving strategy for work applications to find the combined time for two people to paint a room. If Pete takes hours alone and Alicia takes hours alone, let be the hours needed together. In hour, Pete paints of the room, Alicia paints , and together they paint . The rational equation is: Multiply both sides by the LCD, : Distribute and simplify: Converting the improper fraction to a mixed number yields hours. To convert the fractional hour to minutes, multiply by and round to the nearest minute to get minutes. It would take Pete and Alicia about hours and minutes working together.
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Intermediate Algebra @ OpenStax
Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax
Algebra
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Work Application
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Problem-Solving Strategy for Work Applications
Solving a Work Application: Printing Presses
Solving a Work Application: Painting a Room
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Learn After
A maintenance supervisor is scheduling two technicians to paint a lobby. Technician A can complete the job in hours alone, and Technician B can complete it in hours alone. To calculate the total hours they will need while working together, which equation correctly represents the sum of their individual hourly work rates?
A renovation supervisor is using the rational equation to estimate how long it will take a Lead Painter (who takes 10 hours alone) and an Assistant (who takes 8 hours alone) to finish a room together. Match each mathematical component with its corresponding meaning in this workplace scenario.
A project supervisor at a maintenance firm is standardizing the procedure for calculating shared task completion times for the painting crew. Arrange the steps of the problem-solving strategy in the correct order to determine the combined time required for two employees to finish a job together.
A maintenance supervisor uses the work equation to coordinate a painting project. To clear the fractions and begin solving for the total completion time , both sides of the equation must be multiplied by the Least Common Denominator (LCD), which is ____.
When scheduling a facility maintenance project, if one technician takes 10 hours to paint a room alone and another technician takes 8 hours alone, the equation to find their combined completion time is set up as .