Question 955016
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.