Joe and Renee are building a fence. Joe can build the 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?
Answers
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
Given : Joe and Renee are building a fence. Joe can build the 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
To Find : How long would it take Renee to build the fence alone?
Solution:
Joe can build the fence alone in 4 hours
=> Joe work in 1 hr = 1/4
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.
=> Joe worked for 2 hr + 90 mins
= 2 + 90/60
= 2 + 3/2
= 7/2 hrs
Work done by joe in 7/2 = (1/4)(7/2) = 7/8
work done by Renne = 1 - 7/8 = 1/8
Work done by renne in 90 mins (3/2) hr = 1/8
=> Work done by renne in 1 hr = (1/8)/(3/2)
= 1/12
Renne will complete the work alone in1 2 hrs
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