Darcy and Jimboy together can paint 1/4 of a house for 1 day.
Jimboy alone : 1 / x for 1 day.
Darcy: 1 / ( x + 6 ) for 1 day.
Therefore:
1 / x + 1 / ( x + 6 ) = 1 / 4 / ·4 x ( x + 6 ) - multiply both sides by 4x(x+6)
4 ( x + 6 ) + 4 x = x ( x + 6 )
4 x + 24 + 4 x = x² + 6 x
8 x + 24 = x² + 6 x
x² - 2 x - 24 = 0
x² - 6 x + 4 x - 24 = 0
x ( x - 6 ) + 4 ( x - 6 ) = 0
( x - 6 ) ( x + 4 ) = 0
x = 6, or x = - 4 ( can˙t be the negative number )
So: Jimboy : for 6 days.
Darcy: 6 + 6 = 12 days.
Answer: It would take Darcy 12 days to finish the job alone.