Question 730880
Let 


x = number of hours it takes Jake to do the job if he worked alone


y = number of hours it takes Steve to do the job if he worked alone


We are told that "Jake can cut and split a cord of firewood in 6 fewer hours than Steve", so


x = y - 6


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"When they work together, it takes them 4 hours", we can construct this equation


1/x + 1/y = 1/4


4xy(1/x) + 4xy(1/y) = 4xy(1/4) ... multiply EVERY term by the LCD 4xy to clear out the fractions


4y + 4x = xy


4y + 4(y-6) = (y-6)y ... plug in x = y-6


4y + 4(y-6) = (y-6)y


4y + 4y - 24 = y^2-6y


8y - 24 = y^2-6y


0 = y^2-6y-8y+24


0 = y^2-14y+24


y^2-14y+24 = 0


(y-12)(y-2) = 0


y-12 = 0 or y-2 = 0


y = 12 or y = 2


So the possible solutions for y are


y = 12 or y = 2


If y = 2, then 


x = y - 6


x = 2 - 6


x = -4


So y CANNOT be 2 because this makes x a negative number.


So toss out y = 2 as a solution


If y = 12, then


x = y - 6


x = 12 - 6


x = 6


So if y = 12, then x = 6


Therefore, 


Jake can do the job in <font color="red">6 hours</font> if he worked alone. 


Steve can do the job in <font color="red">12 hours</font> if he worked alone.