Question 353840
Leah and Gellie can finish a project in 4 hours if they worked together. 
If it would take Leah 6 hours more than Gellie to finish the project alone, how long would Leah need to finish the project working alone?
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together rate = 1/4 hr/job
Gellie rate = 1/x hr/job
Leah rate = 1/(x+6) hr/job
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Equation:
rate + rate = together rate
1/x + 1/(x+6) = 1/4
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Multiply thru by 4x(x+6) to get:
4(x+6) + 4x = x(x+6)
8x+24 = x^2+6x
x^2 - 2x -24 = 0
Quad Formula:
x = [2 +- sqrt(4-4*-24)]/2
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x = [2 +- sqrt(100)]/2
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Positive solution:
x = 1 + 5 = 6
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Gellie time to do the job: x = 6 hrs
Leah time to do the job: x+6 = 12 hrs
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Cheers,
Stan H