document.write( "Question 1197748: When A,B and C work together, they can finish
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Algebra.Com's Answer #831145 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "When A,B and C work together, they can finish installing the garden in 3 days.
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document.write( "Let  \"a\"  be the A's rate of work, in job per day;\r\n" );
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document.write( "     \"b\"  be the B's rate of work, in job per day;\r\n" );
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document.write( "     \"c\"  be the C's rate of work, in job per day.\r\n" );
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document.write( "From the condition, we have this system of 3 equations in 3 unknowns\r\n" );
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document.write( "    a + b + c = ,           (1)\r\n" );
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document.write( "    4a + 10c = 1,             (2)\r\n" );
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document.write( "    5b +  3c = 1.             (3)\r\n" );
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document.write( "To solve, express  a =   from (2), and express  b =   from (3).\r\n" );
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document.write( "Substitute these expressions into equation (1).  You will exclude \"b\" and \"c\" from (1)\r\n" );
document.write( "and will get single equation for unknown \"c\"\r\n" );
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document.write( "     +  + c = .      (4)\r\n" );
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document.write( "Multiply both sides by 60\r\n" );
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document.write( "    15(1-10c) + 12*(1-3c) + 60c = 20\r\n" );
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document.write( "    15 - 150c + 12 - 36c + 60c = 20\r\n" );
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document.write( "    27 - 126c = 20\r\n" );
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document.write( "    27 - 20 = 126c\r\n" );
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document.write( "       7    = 126c\r\n" );
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document.write( "       c    =  = .\r\n" );
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document.write( "It means that C will complete the job in 18 days working alone.\r\n" );
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document.write( "Now   a =  =  =  = ;\r\n" );
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document.write( "      b =  =  =  = .\r\n" );
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document.write( "ANSWER.  A can complete the job in 9 days working alone;\r\n" );
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document.write( "         B can complete the job in 6 days working alone;\r\n" );
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document.write( "         C can complete the job in 18 days working alone.\r\n" );
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