Question 689322
it takes Tom 9 hours working alone to stucco the walls of his home. It takes Todd 12 hours to do the same amount of work. Tom worked on a house for 4 hours by himself and then Todd joined him to finish the job.  How many more hours did it take to complete the job?

<pre>
We are given Tom's stuccoing rate as 1 job per 9 hours, or
{{{(1_JOB)/(9_HOURS)}}} or {{{1/9}}}{{{JOB/HR)}}}

We are given Todd's stuccoing rate as 1 job per 12 hours, or
{{{(1_JOB)/(12_HOURS)}}} or {{{1/12}}}{{{JOB/HR)}}}

Let X = the number of hours it will take to finish the job after Todd
joins in.

So Todd will have worked only X hours whereas Tom will have worked 4 hours
before Todd joined him, so the X hours are added to the 4 hours Tom has 
already worked, or Tom has worked a total of 4+X hours.

The fraction of the job that Tom did equals his rate times his time, or

{{{1/9}}}{{{JOB/HR)}}}{{{""*""}}}{{{(4+X_HR)}}} or {{{(4+X)/9}}}{{{JOB)}}}

The fraction of the job that Todd did equals his rate times his time, or

{{{1/12}}}{{{JOB/HR)}}}{{{""*""}}}{{{(X_HR)}}} or {{{X/12}}}{{{JOB)}}} 

The equation comes from:

      {{{(matrix(7,1,

The,fraction, of,the, job,Tom,did))}}}{{{""+""}}}{{{(matrix(7,1,

The,fraction, of,the, job,Todd,did))}}}{{{""=""}}}{{{(matrix(3,1,

One,complete,job))}}}.

              {{{(4+X)/9}}}{{{""+""}}}{{{X/12}}}{{{""=""}}}{{{1}}}

Solve that by multiplying through by the LCD of 36.

Answer: {{{20/7}}} hours or {{{2&6/7}}} hours or about 2 hours 52 minutes 

Edwin</pre>