Question

two painters are working together and can paint a house in 3 hours. One painter alone can paint the same house in 8 hours. How many hours would it take the second painter to paint the house by himself

Answer 1

For this case, the first thing we must do is define a variable.
We have then:
x: number of hours it takes the second painter to paint the house working alone.
We have then that the equation that models the problem is:

`(1)/(x) + (1)/(8) = (1)/(3)`
From here, we clear the value of x.
We have then:

`(8x)/(x) + (8x)/(8) = (8x)/(3)`

`8 + x = (8x)/(3)`

`24 + 3x = 8x`

`24 = 8x-3x 24 = 5x`

`x = (24)/(5)`

`x = 4.8`
Answer:
It would take the second painter to paint the house by himself about 4.8 hours.