please help me answer this question ! [urgent]

Question

Virginia can complete her company’s monthly report 5 hours less than the time of Carl. If they work together, the report will take them 6 hours to finish. How long would it take Virginia, working alone? Recall that rate of work is equal to work done over time it takes to complete that work.

Answer 1

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