Question 777735
<pre>
Jobs done = (rate)×(time), or rather 
 
{{{(matrix(5,1,

Fraction,of,a,job,done))}}}{{{""=""}}}{{{(matrix(10,1,

Work,rate,as,the,fraction,of,a,job,per,day))}}}{{{""*""}}}{{{(matrix(4,1,
Number,of,days,worked))}}}

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

A's rate is {{{1/12}}} of a job per day.
B's rate is {{{1/6}}} of a job per day.
C's rate is {{{1/3}}} of a job per day.

A&B's combined rate is 

{{{1/12}}}+{{{1/6}}} = {{{1/12}}}+{{{2/12}}} = {{{3/12}}} = {{{1/4}}} of a job per day.

A&B&C's combined rate is 

{{{1/12}}}+{{{1/6}}}+{{{1/3}}} = {{{1/12}}}+{{{2/12}}}+{{{4/12}}} = {{{7/12}}} of a job per day.

When A&B worked for 1 day they did: 

rate×time = {{{1/4}}}·1 = {{{1/4}}} of the job.

That left {{{3/4}}} 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 = {{{7/12}}}X 

and that must equal the remaining {{{3/4}}} of the job

So the equation is {{{7/12}}}X = {{{3/4}}}

Multiply both sides by 12

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

Edwin</pre>