document.write( "Question 1163797: If A and B work on a project, they need 8 1/9 days. A worked alone for 8 days then B worked alone for 10 days and finished the project. In how many days can A complete the project alone? B? \n" ); document.write( "

Algebra.Com's Answer #788017 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "If A and B work on a project, they need 8 1/9 days. A worked alone for 8 days then B worked alone for 10 days
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document.write( "Let \"a\" be the rate of work of A, i.e. the part of work which A makes per day.\r\n" );
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document.write( "Let \"b\" be the rate of work of B, i.e. the part of work which B makes per day.\r\n" );
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document.write( "First statement of the problem says that the combined rate of work of A and B, working together,\r\n" );
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document.write( "is the value reciprocal to  8 = \r\n" );
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document.write( "    a + b = .            (1)\r\n" );
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document.write( "The second statement of the problem says that\r\n" );
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document.write( "    8a + 10b = 1.           (2)\r\n" );
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document.write( "    Thus the setup is completed, and you have now two equations for two unknowns \"a\"  and  \"b\".\r\n" );
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document.write( "To solve this system of equations, multiply equation (1) by 8 (both sides).  Keep equation (2) as is.\r\n" );
document.write( "You will get then\r\n" );
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document.write( "    8a +  8b =           (3)\r\n" );
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document.write( "    8a + 10b = 1             (4)\r\n" );
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document.write( "Next, subtract equation (3) from equation (4) (both sides).   You will get\r\n" );
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document.write( "          10b - 2b = 1 - ,   or\r\n" );
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document.write( "           2b      =  = .\r\n" );
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document.write( "Hence,  b =  = .\r\n" );
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document.write( "It means that B makes    of the job per day;  hence, B needs 146 days to complete the job alone.\r\n" );
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document.write( "Part of the problem is thus solved, and we need to find \"a\" now.\r\n" );
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document.write( "For it, from equation (2) you have\r\n" );
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document.write( "    8a = 1 - 10b = 1 -  = ;\r\n" );
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document.write( "hence,  a =  : 8 = .\r\n" );
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document.write( "It means that A needs   = 8   days to complete the job alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The numbers in the answer are ugly (at least one is ugly), but I checked them against the equations (1) and (2),
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