SOLUTION: A can do a work in 12 days ;B in 6 days and C in 3 days.A and B start working together and after a day,C joins them.The total number of days required to complete the work is (A) 1

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A can do a work in 12 days ;B in 6 days and C in 3 days.A and B start working together and after a day,C joins them.The total number of days required to complete the work is (A) 1      Log On


   

Question 777735: A can do a work in 12 days ;B in 6 days and C in 3 days.A and B start working together and after a day,C joins them.The total number of days required to complete the work is
(A) 16/7 days (B) 9/7 days (C) 15/7 days (D) 8/7 days
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Jobs done = (rate)×(time), or rather 
 
%28matrix%285%2C1%2C%0D%0A%0D%0AFraction%2Cof%2Ca%2Cjob%2Cdone%29%29%22%22=%22%22%22%22%2A%22%22%28matrix%284%2C1%2C%0D%0ANumber%2Cof%2Cdays%2Cworked%29%29

Let's get the work rates in fraction of a job per day:

A's rate is 1%2F12 of a job per day.
B's rate is 1%2F6 of a job per day.
C's rate is 1%2F3 of a job per day.

A&B's combined rate is 

1%2F12+1%2F6 = 1%2F12+2%2F12 = 3%2F12 = 1%2F4 of a job per day.

A&B&C's combined rate is 

1%2F12+1%2F6+1%2F3 = 1%2F12+2%2F12+4%2F12 = 7%2F12 of a job per day.

When A&B worked for 1 day they did: 

rate×time = 1%2F4·1 = 1%2F4 of the job.

That left 3%2F4 of the job still undone.

Then C joined them for X days.

So when A&B&C worked for X days they did:

rate×time = 7%2F12X 

and that must equal the remaining 3%2F4 of the job

So the equation is 7%2F12X = 3%2F4

Multiply both sides by 12

                   28X = 36
                     X = 36/28
                     X = 9/7 days.

Edwin