SOLUTION: Jake can cut and split a cord of firewood in 6 fewer hours than Steve. When they work together, it takes them 4 hours. How long would it take each of them to do the job alone?

Question 730880: Jake can cut and split a cord of firewood in 6 fewer hours than Steve. When they work together, it takes them 4 hours. How long would it take each of them to do the job alone?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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

-------------------------------------------------------

"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 6 hours if he worked alone.

Steve can do the job in 12 hours if he worked alone.
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