Question

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

Answer 1

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.