It takes Darcy 6 days more to paint a house than Jimboy. If they work together, they can finish the same job in 4 days. How long would it take Darcy to finish the job alone?

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.