document.write( "Question 1197111: abbie paints twice as fast as beth and three times as fast as cathie. if it takes them 60 minutes to paint a living room with all three working together,how long would it take each woman working alone? \n" ); document.write( "

Algebra.Com's Answer #830225 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "abbie paints twice as fast as beth and three times as fast as cathie.
\n" ); document.write( "if it takes them 60 minutes to paint a living room with all three working together,
\n" ); document.write( "how long would it take each woman working alone?
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Their rates of work are in proportion A : B : C = 6 : 3 : 2.\r\n" );
document.write( "\r\n" );
document.write( "So, let 2x be the Cathie's rate of work; 3x be Beth's rate of work and 6x be Abbie's rate of work.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "According to the condition, \r\n" );
document.write( "\r\n" );
document.write( "    6x  + 3x + 2x =   of the job\r\n" );
document.write( "\r\n" );
document.write( "         11x      = \r\n" );
document.write( "\r\n" );
document.write( "           x      = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, Abbie's rate of work is    =   of the job per minute;\r\n" );
document.write( "\r\n" );
document.write( "    Beth's  rate of work is    =   of the job per minute;\r\n" );
document.write( "\r\n" );
document.write( "    Cathie  rate of work is    =   of the job per minute.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that Abbie  needs 110 minutes = 1 hour and 50 minutes to complete the job alone;\r\n" );
document.write( "\r\n" );
document.write( "              Beth   needs 220 minutes = 3 hour and 40 minutes to complete the job alone;\r\n" );
document.write( "\r\n" );
document.write( "              Cathie needs 330 minutes = 5 hour and 30 minutes to complete the job alone.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "As this problem is twisted, it shows me that it is slightly higher that the average school level (with a claim).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Therefore, my response is written in an adequate style, without chewing.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );