SOLUTION: Juan can do 2 jobs in 4 days, and Sergio can 4 jobs in 5 days. One hundred seven jobs need to be done. If Juan works for 6 days and then Sergio begins to help, how long will they w

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Question 1157001: Juan can do 2 jobs in 4 days, and Sergio can 4 jobs in 5 days. One hundred seven jobs need to be done. If Juan works for 6 days and then Sergio begins to help, how long will they work together to finish the 107 jobs?
Please show work thanks!!
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That means, Juan does 1%2F2 job per day and Sergio 4%2F5 jobs per days.


%281%2F2%29%2A6%2B%281%2F2%2B4%2F5%29%2Ax=107----------solve for x.
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3%2B%281%2F2%2B4%2F5%29x=107
%281%2F2%2B4%2F5%29x=104
10%281%2F2%2B4%2F5%29x=1040
%285%2B8%29x=1040
13x=1040
x=80

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Jaun's rate of working is:
+2%2F4+=+1%2F2+ jobs/days
In 6 days he can do:
+%28+1%2F2%29%2A6+=+3+ jobs
---------------------------
+107+-+3+=+104+ jobs left to be done
Let +t+ = time in days to do
+104+ jobs working together
Add their rates working together:
+1%2F2+%2B+4%2F5+=+104%2F+t+
Multiply both sides by +10t+
+5t+%2B+8t+=+1040+
+13t+=+1040+
+t+=+80+
It will take them 80 days working together to finish
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check:
+1%2F2+%2B+4%2F5+=+104+%2F+t+
+.5+%2B+.8+=+104%2F80+
+1.3+=+1.3+
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check my math and get a 2nd opinion if needed