SOLUTION: Joe and Renee are building a fence. Joe can build a fence alone in 4 hours. If Renee starts helping Joe after he has already worked on the fence for 2 hours, they will finish the f

Question 1031208: Joe and Renee are building a fence. Joe can build a fence alone in 4 hours. If Renee starts helping Joe after he has already worked on the fence for 2 hours, they will finish the fence 90 minutes after she joins him. How long would it take Renee to build the fence alone?
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
in 1 hour J does (1/4)
Renee builds (1/x) per hour
(2/4)+(1.5/4)+(1.5/x)=1; the two hours that Joe has worked, the additional 1.5 he works and 1.5 for Renee.
multiply everything by 4x to clear fractions
2x+1.5x+6=4x
.5x=6
x=12 hours for Renee
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
What fraction of the fence does Joe get
done in 2 hrs working alone?
----------------------------
Joe's rate: [ 1 fence built ] / [ 4 hrs ]

Joe builds 1/2 of the fence in 2 hrs
There is 1/2 of the fence left to build
------------------------------
Renee joins Joe. They do 1/2 fence
in min = hrs
Their rate working together:
[ 1/2 fence ] / [ 3/2 hrs ]
-----------------------
Let = Renee's time working alone
to finish 1 fence.
---------------
Add their rates working alone to get rate
working together:
----------------

Multiply both sides by

Working alone, Renee can finish the fence in 12 hrs
----------------
check:

OK
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