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.
