document.write( "Question 958982: three men A B C working together can do a job in 6 hrs less time than A alone, in 1 hr less time than B alone and in one half the time needed by C when working alone. then A and B together can do a job in ____ minutes. \n" ); document.write( "

Algebra.Com's Answer #586085 by Edwin McCravy(20056) $\"\"$ $\"About$

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three men A B C working together can do a job in 6 hrs less time than A alone, in 1 hr less time than B alone and in one half the time needed by C when working alone. then A and B together can do a job in.
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document.write( "Let x = the number of hours it takes A to do 1 job working alone.\r\n" );
document.write( "Let y = the number of hours it takes B to do 1 job working alone.\r\n" );
document.write( "Let z = the number of hours it takes C to do 1 job working alone.\r\n" );
document.write( "Let t = the number of hours it takes A,B, and C to do 1 job working together.\r\n" );
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document.write( "Then\r\n" );
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\n" ); document.write( "three men A B C working together can do a job in 6 hrs less time than A alone,
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document.write( "      t = x - 6\r\n" );
document.write( "(1)   x = t + 6\r\n" );
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\n" ); document.write( "in 1 hr less time than B alone
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document.write( "      t = y - 1\r\n" );
document.write( "(2)   y = t + 1\r\n" );
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\n" ); document.write( "and in one half the time needed by C when working alone.
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document.write( "      t =  \r\n" );
document.write( "     2t = z\r\n" );
document.write( "(3)   z = 2t      \r\n" );
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document.write( "A's working rate =   \r\n" );
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document.write( "B's working rate =  \r\n" );
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document.write( "C's working rate =  \r\n" );
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document.write( "The combined working rate of all three working together =  \r\n" );
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document.write( "    \r\n" );
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document.write( "(4)      \r\n" );
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document.write( "Substituting from (1), (2), and (3) into (4)\r\n" );
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document.write( "        \r\n" );
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document.write( "Multiply through by the LCD, and get t =  hour, after dicarding\r\n" );
document.write( "the negative value for t.\r\n" );
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document.write( "Substituting in (1), (2), and (3) we get that\r\n" );
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document.write( "A can do 1 job in 20/3 hours.\r\n" );
document.write( "B can do 1 job in 5/3 hours.\r\n" );
document.write( "C can do 1 job in 4/3 hours.\r\n" );
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document.write( "But that's not what we are asked to find. What we are asked to find is\r\n" );
document.write( "given by this sentence:\r\n" );
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\n" ); document.write( "A and B together can do a job in ____ hours.
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document.write( "A's working rate =    \r\n" );
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document.write( "B's working rate =     \r\n" );
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document.write( "Suppose it takes them h hours to complete the job.  Then\r\n" );
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document.write( "The combined working rate of A&B working together =  \r\n" );
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document.write( "  \r\n" );
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document.write( "  \r\n" );
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document.write( "Multiply through by an LCD, solve and get h = 4/3 hr or 1 hour and 20 minutes.\r\n" );
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document.write( "Edwin

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