X = number of days it would take Kate to paint the house by herself. . <span>x+5 = number of days it would take Jean to paint the house by herself.</span> <span>Together, they paint the house in 6 days: </span> <span>1/x + 1/(x+5) = 1/6 </span> <span>Multiply both sides by 6x(x+5) </span> <span>6(x+5) + 6x = x(x+5) </span> <span>12x + 30 = x^2 + 5x </span> <span>x^2 − 7x − 30 = 0 </span>therefore the answer is A.
The question is based in pigeonhole principle that says If n or more pigeons are distributed among k >0 pigeonholes,then at least one pigeonhole contains at least pigeons.
