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Question 955016: three men A,B and C can complete a job in 8,12,16 days respectively. A , B can work together for 3 days. then B leaves and C joins.in how many days ,can A and C finish the work?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it will take A and C another 2 days to finish the job.
here's why:
A takes 8 days.
B takes 12 days.
C takes 16 days.
from that, you get:
A can do 1/8 of the job in 1 day.
B can do 1/12 of the job in 1 day.
C can do 1/16 of the job in 1 day.
A and B work together for 3 days.
rate * time = quantity
rate = combined rate of A and B.
quantity = 1 job.
when Q = 1, the job is done.
formula becomes (1/8 + 1/12) * 3 = Q
least common denominator of 8 and 12 is 24.
formula becomes (3/24 + 2/24) * 3 = Q
combine like terms to get:
5/24 * 3 = Q
solve for Q to get Q = 15/24
A and B working together finish 15/24 of the job in 3 days.
that leaves 9/24 of the job to be done because 15/24 + 9/24 = 24/24 = 1.
A and C work together to finish 9/24 of the job.
since the rate for A is 1/8 of the job in one day and the rate for C = 1/16 of the job in one day, then formula of rate * time = quantity becomes:
(1/8 + 1/16) * t = 9/24
least common denominator of 8 and 16 and 24 is 48.
formula becomes:
(6/48 + 3/48) * t = 18/48
combine like terms to get:
9/48 * t = 18 / 48
multiply both sides of the equation by 48/9 to get:
t = 18/48 * 48/9
solve for t to get t = 2
A and C working together finish 9/24 of the job in 2 days.
you have 3 days for A and B working together and 2 days for A and C working together.
from A and B working together, we got 3 * 5/24 = 15/24.
from B and C working together, we got 2 * 9/48 = 18/48 = 9/24.
15/24 + 9/24 = 24/24 = 1
when Q is equal to 1, the job is done.
solution is confirmed.
A and C take 2 days to finish the job.
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