SOLUTION: Greg and Joan are trying to decide whether to take on a job that is scheduled to take them 8 days to complete if they work together. The problem is, that while this is a very well

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Greg and Joan are trying to decide whether to take on a job that is scheduled to take them 8 days to complete if they work together. The problem is, that while this is a very well       Log On


   

Question 1083622: Greg and Joan are trying to decide whether to take on a job that is scheduled to take them 8 days to complete if they work together. The problem is, that while this is a very well paying job, they have only 8 days of vacation and they don’t wish to spend the whole vacation working. But they do need the money. . . To their joy, Brenda said that she could use some extra income too, and she’d like to join them in the job. Assuming the friends all work at the same rate, how much time will the job take all three friends to complete if they work together?
Found 3 solutions by josmiceli, Boreal, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
All 3 work at the same rate:
In words, the rate is:
[ job done, or fraction of the job done ] / [ the time to do it ]
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Let +t+ = time for either Greg or Joan to do 1 job
I can add their rates of working to get their rate
working together
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+1%2Ft+%2B+1%2Ft+=+1%2F8+
+2%2A%28+1%2Ft+%29+=+1%2F8+
+1%2Ft+=+1%2F16+
+t+=+16+
--------------------------
For all 3 friends:
Let +T+ = time to finish the job if
all 3 work on it
+1%2Ft+%2B+1%2Ft+%2B+1%2Ft+=+1%2FT+
+3%2A%28+1%2F16+%29+=+1%2FT+
Multiply both sides by +16T+
+3T+=+16+
+T+=+16%2F3+
It will takes them 3 and 1/3 days working together
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Get another opinion on this if needed

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Greg and Joan need 8 days, so in 1 day they do 1/8 of it
Brenda needs 8 days, so in 1 day she does 1/8 of it.
It takes them x days
x/8+x/8=1
multiply by 8
2x=8
x=4 days
It will take them 4 days.

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
Greg and Joan are trying to decide whether to take on a job that is scheduled to take them 8 days to complete if they work together. The problem is, that while this is a very well paying job, they have only 8 days of vacation and they don’t wish to spend the whole vacation working. But they do need the money. . . To their joy, Brenda said that she could use some extra income too, and she’d like to join them in the job. Assuming the friends all work at the same rate, how much time will the job take all three friends to complete if they work together?
Each person takes 16 hours, alone, to complete job

Correct answer: Time taken by the trio, working together: highlight_green%28matrix%281%2C2%2C+5%261%2F3%2C+days%29%29

IGNORE all other INCORRECT and/or RIDICULOUS answers.