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!