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.
|
|
|
