SOLUTION: Working alone, Alex can build a fence in 8 hours, and Danny can build the same fence in 16 hours. If after working alone for 2 hours, Alex is joined by Danny, how many more hours

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Working alone, Alex can build a fence in 8 hours, and Danny can build the same fence in 16 hours. If after working alone for 2 hours, Alex is joined by Danny, how many more hours       Log On


   

Question 600593: Working alone, Alex can build a fence in 8 hours, and Danny can build the same fence in 16 hours. If after working alone for 2 hours, Alex is joined by Danny, how many more hours will it take the two of them to complete the fence?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What part of the job does Alex get done in
2 hours?
Alex's rate of working is ( 1 fence ) / ( 8 hrs )
The fraction of the job done is +%281%2F8%29%2A2+=+1%2F4+
There is 3/4 of the job left to do
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Add their rates of working to get their rate working together
+1%2F8+%2B+1%2F16+=+%283%2F4%29%2Ft+ ( where t is in hrs )
Multiply both sides by +4t+
+t%2A%28+4%2F8+%2B+4%2F16+%29+=+3+
Multiply both sides by +16+
+t%2A%28+8+%2B+4+%29+=+48+
+t+=+48+%2F+12+
+t+=+4+
It will take both of them 4 hrs to complete the fence