Two constructors

Question

Two constructors working together finished building a room in 6 days. How long would it take for each constructor to build the room by himself, if it is known that one of them would require 9 more days than the other?

Answer 1

THeir combined work-rate is 1/6

But one takes 9 days longer than the other.

1/x + 1/(x+9 ) = 1/6

6(x+9) + 6x = x(x+9)

6x + 54 + 6x = x^2 + 9x

12x + 54 = x^2 + 9x

0 = x^2 + 9x - 12x - 54

0 = x^2 - 3x - 54

0 = (x - 9)( x + 6 )

x-9 = 0 or x+6=0

x=9 or x=-6 <-- disqualified

1/9 + 1/18 = 2/18 + 1/18 = 3/18 = 1/6

The faster one takes 9 days while the slower takes 18 days