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

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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)   (Show Source): You can put this solution on YOUR website!
Jobs done = (rate)×(time), or rather 
 


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

A's rate is  of a job per day.
B's rate is  of a job per day.
C's rate is  of a job per day.

A&B's combined rate is 

+ = + =  =  of a job per day.

A&B&C's combined rate is 

++ = ++ =  of a job per day.

When A&B worked for 1 day they did: 

rate×time = ·1 =  of the job.

That left  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 = X 

and that must equal the remaining  of the job

So the equation is X = 

Multiply both sides by 12

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

Edwin
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