SOLUTION: 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?

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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