Mahmut S. answered 08/14/21
SAT Math Expert
Hello Micah.
Let's say Virginia completes the work alone in x hours. The equation should be;
1/x +1/(x+5) = 1/6; (get the common denominator)
(x+5 +x) = 1 (use cross multiplication)
x*(x+5) 6
6*(2x +5) = x*(x+5)
12x +30 = x2 +5x (cancel left part to create a polynomial)
x2 -7x -30 = 0. (you need to factor this; check factors of -30 which sum of these gives us -7)
(if you choose -30 = -10*3; you get the right pair of factors because -10 +3 = -7 in the middle)
x2 -7x -30 = (x-10)(x+3) = 0;
x-10 = 0; x =10 or x +3 = 0; x = -3
x has to be 10 since time can not be -3.
hope that helps