Question

It would take Delia 3 hours longer to re tile their bathroom by herself than it would for kari to retile on her own. If they work together it would take them 2 hours to retile their bathroom. How long would it take for Delia to retile the bathroom alone?

Answer 1

6hours

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?

∴

`(1)/(x)+(1)/(3+x)= (1)/(2)`

`(x+3+x)/(x(3+x))= (1)/(2)`

`(2x+3)/(3x+x^2)= (1)/(2)`

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