document.write( "Question 1184062: Ron and Sam take 1 hour to paint 7/12 of the living room. Sam and Tom take 1 hour to paint 8/15 of the living room. Ron and Tom take 1 hour to paint 9/20 of the living room. How long will it take for Ron, Sam and Rom to paint the living room together? \n" ); document.write( "

Algebra.Com's Answer #814605 by ikleyn(52931) $\"\"$ $\"About$

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\n" ); document.write( "Ron and Sam take 1 hour to paint 7/12 of the living room.
\n" ); document.write( "Sam and Tom take 1 hour to paint 8/15 of the living room.
\n" ); document.write( "Ron and Tom take 1 hour to paint 9/20 of the living room.
\n" ); document.write( "How long will it take for Ron, Sam and Rom to paint the living room together?
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document.write( "Let r be the Ron's rate of work (in parts of the living room per hour);\r\n" );
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document.write( "    s be the Sam's rate of work,  and\r\n" );
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document.write( "    t be the Tom's rate of work.\r\n" );
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document.write( "From the condition, we have  \r\n" );
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document.write( "    r + s = 7/12     (1)\r\n" );
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document.write( "    s + t = 8/15     (2)\r\n" );
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document.write( "    r + t = 9/20     (3)\r\n" );
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document.write( "Add the equations (1), (2) and (3). You will get\r\n" );
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document.write( "    \r\n" );
document.write( "    2(r + s + t) =  =  = 94/60.\r\n" );
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document.write( "Hence,\r\n" );
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document.write( "     r + s + t = 47/60.\r\n" );
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document.write( "It means that Ron, Sam and Tom will complete painting the room in   hours = 1  hours.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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