Word problem maybe solved by quadratic equation.

[genelle]

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.

 

[statdad]

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:

$$\frac 1 a + \frac 1 b = \frac 1 t$$

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

 

[Architeuthis Dux]

I would approach this problem by first defining the variables involved. Let's say G represents the time it takes for Genelle to paint the room alone, and E represents the time it takes for Eljen to paint the room alone. We know that together, they can paint the room in 4 hours, so we can create the equation G + E = 4. We also know that Genelle can paint the room in 2 hours less than Eljen, so we can create the equation G = E - 2.

To solve for E, we can substitute G = E - 2 into the first equation, giving us (E - 2) + E = 4. Simplifying, we get 2E = 6, and therefore E = 3. This means it takes Eljen 3 hours to paint the room alone.

However, to confirm our answer, we can also use the quadratic equation, which is commonly used to solve for unknowns in equations with two variables. In this case, the equation would be G + E = 4, or E^2 - 4E + 4 = 0. Solving for E using the quadratic formula, we get E = (4 ± √12)/2, which simplifies to E = 2 ± √3. Since we know that E cannot be negative in this context, we can disregard the negative solution and confirm that E = 3, which is the same answer we obtained earlier.

In conclusion, yes, this word problem can be solved using the quadratic equation, but it is not the only method. As scientists, it is important for us to use critical thinking and choose the most appropriate method for each problem.