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Question 165899: A can do a certain job in 4 hrs, B in 6 hrs, C in 8 hrs. How long will it take to do the job if A&B work in 1 hr & B&C finish the job.
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=amount of time it takes B&C to finish the job
A works at the rate of 1/4 job per hour ((1/4)*4=1 job)
B works at the rate of 1/6 job per hour
A&B work at the rate of 1/4 + 1/6 =3/12 +2/12=5/12 of the job per hour
C works at the rate of 1/8 job per hour
B&C works at the rate of 1/6 + 1/8=4/24 + 3/24=7/24 of the job per hour
In 1 hour, A&B completes (5/12)*1 or 5/12 of the job leaving
12/12 -5/12=7/12 of the job for B&C to finish
So, our equation to solve is:
(7/24)*x=7/12 (7/12 of the job, that is) multiply each term by 24
7x=14 divide each side by 7
x=2 hours------------------amount of time it takes B&C to finish
Total time, then would be 1+2=3 hours
CK
In 1 hour
A&B completes (5/12)*1=5/12 of the job
In 2 hours:
B&C completes (7/24)*2=7/12 of the job
So, 5/12 +7/12=12/12=1 job
Hope this helps-----ptaylor
B&C works at the rate of
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