Word problem maybe solved by quadratic equation.

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SUMMARY

The discussion centers on solving a word problem involving two individuals, Genelle and Eljen, who can paint a room together in 4 hours. Genelle takes 2 hours less than Eljen to complete the task alone. The solution requires the application of the quadratic equation to establish a relationship between their individual work rates. The equation 1/a + 1/b = 1/t is essential for determining the time it takes Eljen to paint the room alone.

PREREQUISITES
  • Understanding of quadratic equations
  • Knowledge of work rate concepts
  • Ability to set up equations based on given conditions
  • Familiarity with algebraic manipulation
NEXT STEPS
  • Study the application of the quadratic formula in real-world problems
  • Learn how to derive work rate equations for multiple workers
  • Practice solving word problems involving rates and time
  • Explore advanced topics in algebra, such as systems of equations
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Students studying algebra, educators teaching quadratic equations, and anyone interested in applying mathematical concepts to solve practical problems.

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Homework Statement


Here the the word problem:
Genelle and Eljen can paint a room together in 4 hours. Working alone, Genelle can paint the room in two hours less than Eljen can. Find how long it takes Eljen to paint the room alone.

Homework Equations


Maybe, this problem can be solved using the quadratic equation.

The Attempt at a Solution


Please.. it's about quadratic erquation.
 
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A general approach in these is to think about the RATES of work. If you have two people, say A and B, who require a hours and b hours when working alone to finish a job, and t hours when working together, the numbers a, b, and t are connected with this equation:

<br /> \frac 1 a + \frac 1 b = \frac 1 t<br />

Use the information provided in your question to set up the unknowns, and then the appropriate equation.
 

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