SOLUTION: 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

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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?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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? 
We are given Tom's stuccoing rate as 1 job per 9 hours, or
%281_JOB%29%2F%289_HOURS%29 or 1%2F9JOB%2FHR%29

We are given Todd's stuccoing rate as 1 job per 12 hours, or
%281_JOB%29%2F%2812_HOURS%29 or 1%2F12JOB%2FHR%29

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%2F9JOB%2FHR%29%22%22%2A%22%22%284%2BX_HR%29 or %284%2BX%29%2F9JOB%29

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

1%2F12JOB%2FHR%29%22%22%2A%22%22%28X_HR%29 or X%2F12JOB%29 

The equation comes from:

      %28matrix%287%2C1%2C%0D%0A%0D%0AThe%2Cfraction%2C+of%2Cthe%2C+job%2CTom%2Cdid%29%29%22%22%2B%22%22%28matrix%287%2C1%2C%0D%0A%0D%0AThe%2Cfraction%2C+of%2Cthe%2C+job%2CTodd%2Cdid%29%29%22%22=%22%22%28matrix%283%2C1%2C%0D%0A%0D%0AOne%2Ccomplete%2Cjob%29%29.

              %284%2BX%29%2F9%22%22%2B%22%22X%2F12%22%22=%22%221

Solve that by multiplying through by the LCD of 36.

Answer: 20%2F7 hours or 2%266%2F7 hours or about 2 hours 52 minutes 

Edwin