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Let x be the time for Jeff to do the job alone.
Then the rate of work for Jeff is of the job per hour;
for Kirk of the job per hour, an
the combined rate of work for both is of the hour.
It gives you an equation
rate of Jeff + rate of Kirk = combined rate, or
+ = .
To solve the equation, multiply both sides by 12x(x+2). You will get
12(x+2) + 12x = x(x+2)
12x + 24 + 12x = x^2 + 2x
x^2 - 22x - 24 = 0.
Apply the quadratic formula
= = .
Only positive root x= 23.0415 makes sense.
Answer. 23.04 hours for Jeff and 25.04 hours for Kirk.
CHECK. = 0.083334; = 0.083333. ! Correct !
Solved.