document.write( "Question 975770: A and B can do a piece of work in 6 days,B and c together in 10 days,c and A together in 7 1/2 days.in how many days can c individually completes the work?
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\n" ); document.write( "A and B can do a piece of work in 6 days, B and C together in 10 days, C and A together in 7 1/2 days.
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document.write( "Let  'a'  be the rate of work for A;\r\n" );
document.write( "     'b'  be the rate of work for B;\r\n" );
document.write( "     'c'  be the rate of work for C.\r\n" );
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document.write( "From the problem, we have this system of equations \r\n" );
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document.write( "    a + b = ,      (1)\r\n" );
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document.write( "    b + c = ,     (2)\r\n" );
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document.write( "    a + c = .    (3)\r\n" );
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document.write( "Add equations (1), (2) and (3).  You will get\r\n" );
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document.write( "    2(a + b + c) =  +  + .    (4)\r\n" );
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document.write( "Multiply both sides of (5) by 60.  Notice that   = 8.  You will get\r\n" );
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document.write( "    120*(a + b + c) = 12 + 6 + 8 = 24,\r\n" );
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document.write( "which implies\r\n" );
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document.write( "    a + b + c = ,\r\n" );
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document.write( "or\r\n" );
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document.write( "    a + b + c = .    (5)\r\n" );
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document.write( "Now, to find 'c', subtract equation (1) from equation (5).  You will get\r\n" );
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document.write( "    c =  -  =  = .\r\n" );
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document.write( "Hence, the C's rate of work is 1/30 of the job per day,\r\n" );
document.write( "which means that C can complete the entire job in 30 days working alone.\r\n" );
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document.write( "ANSWER.  C can complete the entire job in 30 days working alone.\r\n" );
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