Question 729572
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A company contracts to paint 3 houses. Mr.Orange can paint a house in 6 days while Mr.Grey would take 8 days 
and Mr.Red 12 days. After 8 days Mr.Orange goes on vacation and Mr.Grey begins to work for a period of 6 days. 
How many days will it take Mr.Red to complete the contract?
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The whole job is to paint 3 houses.


Mr. Orange' rate of work is  {{{1/6}}}  of the house per day.

Working 8 days, Mr Orange painted  {{{8/6}}} = {{{4/3}}}  houses, and  3 - {{{4/3}}} = {{{5/3}}} houses remained
to paint.



Mr. Gray' rate of work is  {{{1/8}}}  of the house per day.

Working 6 days, Mr. Gray painted  {{{6/8}}} = {{{3/4}}}  of a house, and  

   {{{5/3}}} - {{{3/4}}} = {{{20/12}}} - {{{9/12}}} = {{{11/12}}} of a  house remained to paint.




Mr. Red' rate of work is  {{{1/12}}}  of the house per day.

Hence, he needs 

    {{{((11/12))/((1/12))}}} = 11 days to complete the contract.


<U>ANSWER</U>.  Mr. Red needs 11 days to complete the job.
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Solved.