Answer:
6hours
Step-by-step explanation:
From the given information:
Suppose it took Karl x hours to retile her bathroom,
Then it will take Della 3 hours longer i.e (3+x) hours
If Della and Karl work together or will take them 2 hours
The objective is to determine how long it will take Delia to retile the bathroom alone?
∴
[tex]\dfrac{1}{x}+\dfrac{1}{3+x}= \dfrac{1}{2}[/tex]
[tex]\dfrac{x+3+x}{x(3+x)}= \dfrac{1}{2}[/tex]
[tex]\dfrac{2x+3}{3x+x^2}= \dfrac{1}{2}[/tex]
By cross multiplying, we have:
2(2x+3) = 3x+x²
4x + 6 = 3x + x²
3x + x² - 4x - 6
x² - x - 6 = 0
Using quadratic equation
x² -3x +2x - 6 = 0
x(x - 3) + 2(x - 3) = 0
(x +2) (x - 3) = 0
x + 2 = 0 or x - 3 = 0
x = -2 or x = 3
Since we are concerned about the positive integer,
Then, Karl = x = 3 hours while Della which is (3+x) = 3+3 = 6hours
