document.write( "Question 1046595: When Raul and Rudy work together, they can point a car in 8 days. Also, they could point this car if Raul worked 12 days and Rudy worked 6 days. How long would it take each of them to point the car alone. \n" ); document.write( "

Algebra.Com's Answer #662063 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "When Raul and Rudy work together, they can point a car in 8 days. Also, they could point this car if Raul worked 12 days
\n" ); document.write( "and Rudy worked 6 days. How long would it take each of them to point the car alone.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let \"x\" be the Raul's rate of work and \"y\" be Rudy's rate of work\r\n" );
document.write( "( measured in the unit \"car-per-day,  ).\r\n" );
document.write( "\r\n" );
document.write( "Then from the condition you have this system of two linear equations\r\n" );
document.write( "\r\n" );
document.write( "x + y = ,      (1)    ( \"When Raul and Rudy work together, they can point a car in 8 days.\" )\r\n" );
document.write( "12x + 6y = 1.     (2)    ( \"they could point this car if Raul worked 12 days \r\n" );
document.write( "and Rudy worked 6 days.\" )\r\n" );
document.write( "\r\n" );
document.write( "To solve it, express x =  from (1) and substitute it into (2). You will get\r\n" );
document.write( "\r\n" );
document.write( " + 6y = 1,  or\r\n" );
document.write( "\r\n" );
document.write( "3 - 24y + 12y = 2,  or\r\n" );
document.write( "\r\n" );
document.write( "3 - 12y = 2,  or  3 - 2 = 12y,  or  y = .\r\n" );
document.write( "\r\n" );
document.write( "Thus you found that the Rudy's rate is .  Hence, he need 12 days to complete the job working alone.\r\n" );
document.write( "\r\n" );
document.write( "Next, from (1) x =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "It means that Raul's rate is , and Raul needs 24 days to complete the job working alone.\r\n" );
document.write( "\r\n" );
document.write( "Answer.  Raul needs 24 days to complete the job working alone.\r\n" );
document.write( "         Rudy needs 12 days to complete the job working alone.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "There is a bunch of my lessons on joint work problems with detailed solutions\r
\n" ); document.write( "\n" ); document.write( "    - Rate of work problems,\r
\n" ); document.write( "\n" ); document.write( "    - Using Fractions to solve word problems on joint work,\r
\n" ); document.write( "\n" ); document.write( "    - Solving more complicated word problems on joint work,\r
\n" ); document.write( "\n" ); document.write( "    - Using quadratic equations to solve word problems on joint work,\r
\n" ); document.write( "\n" ); document.write( "    - Solving rate of work problem by reducing to a system of linear equations,\r
\n" ); document.write( "\n" ); document.write( "    - Selected joint-work word problems from the archive \r
\n" ); document.write( "\n" ); document.write( "    - Joint work word problem for the day of April, 1\r
\n" ); document.write( "\n" ); document.write( "    - Joint-work problems for 3 participants.\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solving this kind of problems.\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "which contains many other word problems and many other interesting and useful things.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );