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Question 149524: urgent..
working together, alice and betty can do a certain job in 4 1/3 days. but alice felt ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them worked alone?
thnx for the help
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Alice and Betty works at the rate of 1/(4 1/3) or 1/(13/3)=3/13 job per day
Working together, in 2 days they do(3/13)*2=6/13 of the job, Leaving 7/13 of the job yet to be done. Now we are told that Sally finishes the job in 6 3/4 days which means that she works at the rate of (7/13)/(6 3/4) jobs per day.
(7/13)/(6 3/4)=(7/13)/(27/4)=(7/13)*(4/27)=28/351 jobs per day
Now, we have determined that Sally works at the rate of 28/351 jobs per day
If we let x=Alices rate of work , we have the following equation to solve:
x + 28/351=3/13=81/351 subtract 28/351 from each side
x=81/351 - 28/351=53/351 jobs per day---Alice's rate of work
Now if Sally works at the rate of 28/351 jobs per day, in zs(z sally) days, she does 1 job. so:
(28/351)*zs=1
zs=351/28 =~12.5 days--------time it takes Sally working alone
Now for Alice:
(53/351)*za=1
za=351/53 =~6.6 days-----------time it takes Alice working alone
CK
28/351 + 53/351= 3/13
81/351=3/13
3/13=3/13
Hope that you can follow what I've done---ptaylor
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