document.write( "Question 720244: If Person A can pain the house 6 times as fast as person B. The year A and B worked together it took them 9 days. How long would it take each to paint the house? \n" ); document.write( "

Algebra.Com's Answer #441729 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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If Person A can pain the house 6 times as fast as person B.
\n" ); document.write( " The year A and B worked together it took them 9 days.
\n" ); document.write( " How long would it take each to paint the house?
\n" ); document.write( ":
\n" ); document.write( "let a = time required by person A to paint the house alone
\n" ); document.write( "then it says, A is 6 time faster, or B take 6 times as long, therefore:
\n" ); document.write( "6a = time required by B alone
\n" ); document.write( ":
\n" ); document.write( "Let the completed job = 1
\n" ); document.write( ":
\n" ); document.write( "Each will do a fraction of the job, the two fractions add up to 1
\n" ); document.write( ":
\n" ); document.write( " $\"9%2Fa\"$ + $\"9%2F%286a%29\"$ = 1
\n" ); document.write( "mult by 6a to clear the denominators, resulting in:
\n" ); document.write( "6(9) + 9 = 6a
\n" ); document.write( "54 + 9 = 6a
\n" ); document.write( "63 = 6a
\n" ); document.write( "a = 63/6
\n" ); document.write( "a = 10.5 days for A alone
\n" ); document.write( "then
\n" ); document.write( "6(10.5) = 63 days B working alone
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "See if that works out
\n" ); document.write( " $\"9%2F10.5\"$ + $\"9%2F63\"$ =
\n" ); document.write( ".857 + .143 = 1 \n" ); document.write( "

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