document.write( "Question 427897: Working alone, two painters, A and B, can paint a building in 12 and 16 days respectively. After they work together for 3 days, A leaves and B continues for 2 more days. Then C joins B and they finish the job in 3 more days. In what time could C do the whole job alone? \n" ); document.write( "

Algebra.Com's Answer #297510 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Working alone, two painters, A and B, can paint a building in 12 and 16 days respectively.
\n" ); document.write( " After they work together for 3 days, A leaves and B continues for 2 more days.
\n" ); document.write( " Then C joins B and they finish the job in 3 more days.
\n" ); document.write( " In what time could C do the whole job alone?
\n" ); document.write( ":
\n" ); document.write( "Let c = time required by c to do the job alone
\n" ); document.write( ":
\n" ); document.write( "Let the completed job = 1
\n" ); document.write( ":
\n" ); document.write( "From the information we know that
\n" ); document.write( "A works for 3 days
\n" ); document.write( "B works 3 + 2 + 3 = 8 days
\n" ); document.write( "C works 3 days
\n" ); document.write( ":
\n" ); document.write( " $\"3%2F12\"$ + $\"8%2F16\"$ + $\"3%2Fc\"$ = 1
\n" ); document.write( "Reduce the fractions a common denominator of 4
\n" ); document.write( " $\"1%2F4\"$ + $\"2%2F4\"$ + $\"3%2Fc\"$ = 1
\n" ); document.write( "Multiply by 4c to clear the denominators, results:
\n" ); document.write( "c + 2c + 4(3) = 4c
\n" ); document.write( ":
\n" ); document.write( "3c + 12 = 4c
\n" ); document.write( ":
\n" ); document.write( "12 = 4c - 3c
\n" ); document.write( ":
\n" ); document.write( "c = 12 days alone is C's time
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this:
\n" ); document.write( " $\"3%2F12\"$ + $\"8%2F16\"$ + $\"3%2F12\"$ =
\n" ); document.write( " $\"1%2F4\"$ + $\"2%2F4\"$ + $\"1%2F4\"$ = 1; confirms our solution of 12 days \n" ); document.write( "

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