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Question 709419: Workers A and B, working together, can finish a job in 8 hours. If they work together for 6 hours after which Worker A leaves, then Worker B needs 9 more hours to finish the job. How long does it take Worker A to do the job alone?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=amount of time needed for worker A to complete the job working alone
And y=amount of time needed for worker B to complete the job working alone
Worker A works at the rate of 1/x of the job per hour
Worker B works at the rate of 1/y of the job per hour
Together they work at the rate of 1/8 of the job per hour, soooo
1/x + 1/y = 1/8----------------eq1
If they work together for 6 hours, they complete 6*(1/8)=6/8=3/4 of the job leaving 1/4 of the job to be completed
When worker A leaves, worker B completes 1/4 of the job in 9 hours, or
9*(1/y)=1/4-----------eq2
We can simplify both equations:
Eq1: multiply each term by 8xy:
8x+8y=xy----eq1a
Eq2: multiply each term by 4y:
36=y or
y=36 hours ---time required for worker B working alone to complete the job
substitute y=36 into eq1a:
8x+8*36=36x
28x=288
x=10.29 hours---Time required for A working alone to complete the job
CK
1/(10.29)+1/36=1/8
0.0972+0.028=0.125
0.125~~~~0.125 OK
Hope this helps---ptaylor
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