Question 283915: Arthur can edit 15 essays in 10 hours. Debra needs 15 hours to do the same job. If they work together, how long will it take them edit the essays?
Found 3 solutions by jim_thompson5910, Alan3354, richwmiller:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Since "Arthus can edit 15 essays in 10 hours", this means that in one hour, Arthus gets  of the job is done. Note: in 10 hours,  job is done. So Arthus' rate is of a job an hour (think of this as the "speed")
Also, because "Debra needs 15 hours to do the same job", this means that in one hour, Debra gets  of the job done. So Debra's rate is of a job an hour.
Add the rates to get  . The value  is the rate of the two workers combined. So if Arthus and Debra work together, their rate is of a job an hour. What this means is that in one hour, of the job is done.
Now if we let t = time to get the job done if they work together, then we can multiply the time 't' by this combined rate to get 1 complete job. In other words, 
Now multiply both sides by 6 to get  .
So it will take them 6 hours if they work together.
Notice how  which confirms our answer.
Answer by Alan3354(69443)  (Show Source):
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! x/10+x/15=1
3x+2x=30
5x=30
x=6
they can do them in 6 hours together.
6/10+6/15=1
3/5+2/5=1
Arthur does 3/5 of the job and Debra does 2/5.
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