document.write( "Question 667142: A painter can do a given job in 6 hours. Her helper can do the same job in 10 hours. The painter begins the work and after two hours is joined by the helper. In how many hours will they complete the job? \n" ); document.write( "

Algebra.Com's Answer #414819 by josmiceli(19441) $\"\"$ $\"About$

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A painter can do a given job in 6 hours.
\n" ); document.write( "The painter can do 1/6 of the job in 1 hour
\n" ); document.write( "The painter can do 2/6 or 1/3 of the job in 2 hours
\n" ); document.write( "That means 2/3 of the job is left to be done
\n" ); document.write( "Add their rates of working to get the rate at
\n" ); document.write( "which they can do the remaining 2/3 of a job
\n" ); document.write( "Let $\"h\"$ = hours needed to do the 2/3 of a job
\n" ); document.write( " $\"+1%2F6+%2B+1%2F10+=+%282%2F3%29%2Fh+\"$
\n" ); document.write( " $\"+1%2F6+%2B+1%2F10+=+2%2F%283h%29+\"$
\n" ); document.write( "Multiply both sides by $\"+30h+\"$
\n" ); document.write( " $\"+5h+%2B+3h+=+20+\"$
\n" ); document.write( " $\"+8h+=+20+\"$
\n" ); document.write( " $\"+h+=+5%2F2+\"$
\n" ); document.write( "They will complete the job in 2 and 1/2 hours
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