document.write( "Question 1122907: when a b and c work together they finish installing a garden in 3 days. The job could be completed if A worked 4 days alone and C worked 10 days alone, or if B worked 5 days alone and C worked 3 days alone. How many days would it take each worker, alone, to complete garden?
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Algebra.Com's Answer #739085 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Let \"a\" be the rate of work of A;\r\n" );
document.write( "    \"b\" ---------- ''--------- B:,  and\r\n" );
document.write( "    \"c\" ---------- ''--------- C.\r\n" );
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document.write( "Then from the condition, you have these three equations for 3 unknowns\r\n" );
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document.write( "3a + 3b +  3c = 1,    (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( "The setup is done, which is the key step in the solution.\r\n" );
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document.write( "Now you can use any method to solve the system. For example, you can express \"a\" via \"c\" from (2) and express \"b\" via \"c\" from (3), \r\n" );
document.write( "and then substitute it into eq(1) to find \"c\".\r\n" );
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document.write( "As soon as you find \"c\", you will be able to find each \"a\" and \"b\" separately from eq(2) and eq(3) respectively.\r\n" );
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document.write( "Answer.  a = ,  b = ,  c = .\r\n" );
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document.write( "         It means that A needs 9 days;  B needs 6 days,  and C needs 18 days to complete the job, if everybody works alone.\r\n" );
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