SOLUTION: person A can finish a piece of work in 12hrs less than person B.If they work together 4/9 of the work is done in 5hrs.How long does it take them to do the work?

Question 1036373: person A can finish a piece of work in 12hrs less than person B.If they work together 4/9 of the work is done in 5hrs.How long does it take them to do the work?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
person A can finish a piece of work in 12hrs less than person B.If they work together 4/9 of the work is done in 5hrs.How long does it take them to do the work?
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B's time = x hrs/job ; B's rate 1/x job/hr
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A's time = x-12 hrs/job ; A's rate 1/(x-12) job/hr
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Together rate = (1/x) + 1/(x-12) = [x-12 + x]/[x(x-12)] = (2x-12)/(x^2-12x) job/hr
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Equation:
time*rate = work done
5[(2x-12)/(x^2-12x)] = 4/9
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45(2x-12) = 4x^2-48x
90x - 540 = 4x^2 - 48x
4x^2 - 138x + 540 = 0
x = 30 hrs (time B takes to do the job alone)
x-12 = 18 hrs (time A takes to do the job alone)
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Cheers,
Stan H.
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