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?

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Answer 1 · 2016-06-30T01:23:53

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

$1/(x - 6) + 1/x = 1/4$

$(4x)/(4(x)(x - 6)) + (4(x - 6))/((x - 6)(4)(x)) = 1/4$

$4(4x + 4x - 24 )=4(x^2 - 6x)$

$4(8x - 24) = 4x^2 - 24x$

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

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

$0 = 4(x^2 - 14x + 24)$

$0 = 4(x - 12)(x - 2)$

$x = 12 and 2$

Alone, Jenny can finish the job in $6" hours"$ while Steve takes $12" hours"$ .

Hopefully this helps!