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Question 1068087: A and B are the work of a full 8 days. After 6 days, the two work together, 'A' work left, then 'B' s remaining work to be completed in 6 days. Everyone will have to work out how many days to complete?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A and B can do the whole job in 8 days.
they work together for 6 days.
that means they have completed 6/8 = 3/4 of the job.
A goes away.
B takes another 6 days to complete the remaining 1/4 of the job.
rate * time = quantity of work produced.
for B, this formula becomes rate * 6 = 1/4
solve for rate to get rate = 1/4 / 6 = 1/24.
that's how much of the job that B can complete in one day.
now that you know the rate that B works at, you can find the rate that A works at.
when they work together, they complete the job in 8 days.
when they work together, their rates are additive.
let x = the rate that A works at.
you already know that B works at the rate of 1/24 of the job in one day.
formula of rate * time = quantity of work produced becomes:
(x + 1/24) * 8 = 1
simplify to get 8x + 8/24 = 1
subtract 8/24 from both sides of the equation to get:
8x = 16/24
divide both sides of the equation by 8 to get:
x = 16 / (8 * 24)
solve for x to get x = 2/24
this means that A completes 2/24 of the job in 1 day.
to see if this is correct, use the rate * time formula again.
rate * time = quantity of work produced becomes:
(2/24 + 1/24) * 8 = 1
combine like terms to get 3/24 * 8 = 1
simplify to get 1 = 1
this confirms the solution is correct.
A can complete 2/24 of the job in 1 day.
working at that rate alone, it would take him 12 days to complete the job alone.
2/24 * 12 = 1
simplify to get 1/12 * 12 =1
simplify further to get 1 = 1.
rate that A works at per day is confirmed to be good.
B can complete 1/24 of the job in 1 day.
working at that rate alone, it would take him 24 days to complete the job.
1/24 * 24 = 1
simplify to get 1 = 1
rate that B works at is confirmed to be good.
your solution is:
A can complete 1/12 of the job in one day and it would take him 12 days to complete the job on his own.
B can complete 1/24 of the job in one day and it would take him 24 days to complete the job on his own.
since it takes both of them 8 days to complete the job together, you can confirm the solution is correct.
(1/24 + 2/24) * 8 = 1 becomes 3/24 * 8 = 1 which becomes 1/8 * 8 = 1 which becomes 1 = 1.
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