SOLUTION: 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 fin

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? (Show your solution using Quadratic Equation)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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
----------------
Equation:
rate + rate = together rate
1/x + 1/(x+6) = 1/4
---
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
---
x = [2 +- sqrt(100)]/2
---
Positive solution:
x = 1 + 5 = 6
----
Gellie time to do the job: x = 6 hrs
Leah time to do the job: x+6 = 12 hrs
=====================================
Cheers,
Stan H

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