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

Jun 30, 2016

We have to consider the amount of the task each individual can get done in one hour.

#### Explanation:

$\frac{1}{x - 6} + \frac{1}{x} = \frac{1}{4}$

$\frac{4 x}{4 \left(x\right) \left(x - 6\right)} + \frac{4 \left(x - 6\right)}{\left(x - 6\right) \left(4\right) \left(x\right)} = \frac{1}{4}$

$4 \left(4 x + 4 x - 24\right) = 4 \left({x}^{2} - 6 x\right)$

$4 \left(8 x - 24\right) = 4 {x}^{2} - 24 x$

$32 x - 96 = 4 {x}^{2} - 24 x$

$0 = 4 {x}^{2} - 56 x + 96$

$0 = 4 \left({x}^{2} - 14 x + 24\right)$

$0 = 4 \left(x - 12\right) \left(x - 2\right)$

$x = 12 \mathmr{and} 2$

Alone, Jenny can finish the job in $6 \text{ hours}$ while Steve takes $12 \text{ hours}$.

Hopefully this helps!