Kate and Jean paint a house together in 6 days. If they work alone, Kate takes 5 fewer days than Jean would take to do the same job. Which equation represents the time it takes Kate to paint the house by herself?

A. x^2-7x-30=0

B. x^2-5x-30=0

C. 2x-1=0

D. x^2-5x over 6 = 0

Number of jobs=1

Time:

Since ‘x’ is given as a variable in the choices, we should reserve it for Kate and use ‘y’ for Jean as follows:

Kate: = > x

Jean: = > y

But y = x - 5

Combined rate:

1/x + 1/y

= (x + y) / (xy)

Number of jobs done:

Number of days X combined rate = number of jobs

6 [ (x + y) / (xy) ] = 1

6x + 6y = xy

6x + 6 (x - 5) = x (x - 5)

6x + 6x - 30 = x² - 5x

12x - 30 = x² - 5x

x² - 17x + 30 = 0

Therefore, the answer would be A.