document.write( "Question 1097081: a and b working together can do a given job in 4 days, b and c together can do the job in 3 days and a and c together can do it in 2.4 days. In how many days can each do the job working alone. \n" ); document.write( "

Algebra.Com's Answer #711486 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Let \"a\", \"b\" and \"c\" be the rate-of-work of each of the persons A, B, and C respectively.\r\n" );
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document.write( "We are given that \r\n" );
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document.write( "a + b = ,      (1)\r\n" );
document.write( "b + c = ,      (2)\r\n" );
document.write( "a + c = .    (3)\r\n" );
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document.write( "To solve the system (1), (2), (3), let us start adding the equations (1), (2) and (3).\r\n" );
document.write( "You will get \r\n" );
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document.write( "2a + 2b + 2c =  =  =  = 1.\r\n" );
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document.write( "Hence, \r\n" );
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document.write( "a + b + c = 1/2.    (4)\r\n" );
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document.write( "Thus we just found the combined rate-of-work of the three persons working together. It is  of job per day.\r\n" );
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document.write( "Now we have to find individual rate-of-work for each person. For it, let us first subtract the equation (1) from (4). You will get\r\n" );
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document.write( "c =  = .\r\n" );
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document.write( "Next, subtract the equation (2) from (4). You will get\r\n" );
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document.write( "a =  = .\r\n" );
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document.write( "Finally, subract the equation (3) from (4). You will get\r\n" );
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document.write( "b =  =  =  = .\r\n" );
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document.write( "Answer. The individual rates of work are  for C,  for A and  for B (in job-per-day units).\r\n" );
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document.write( "        So,  A will complete the job in 6 days;  B will complete the job in 12 days;  and C will complete the job in 4 days.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For many other similar solved problems See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Joint-work problems for 3 participants\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this textbook under the topic
\n" ); document.write( "\"Rate of work and joint work problems\" of the section \"Word problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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\n" ); document.write( "Notice. The way on how I solved the system of equations is THE STANDARD WAY of dealing with such special systems.\r
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\n" ); document.write( "\n" ); document.write( "The way that @gosgarithmetic proposes in his solution is the way to NOWHERE.\r
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