document.write( "Question 644105: Sam finish a problem in 7 hours. Peter finish the same project in 3 hours. How long would it take the to finish the project together? \n" ); document.write( "

Algebra.Com's Answer #404815 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "How to do it in your head:\r\n" );
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document.write( "The LCM of 7 and 3 is 21.  If they worked together for 21 hours, \r\n" );
document.write( "Sam would finish 3 projects while Peter would finish 7 projects. \r\n" );
document.write( "So in 21 hours they would finish 10 projects.  So together they \r\n" );
document.write( "could finish just 1 project in just 1/10th of that 21 hours or \r\n" );
document.write( "2.1 hours, or 2 hours, 6 minutes.\r\n" );
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document.write( "How to do it with algebra:\r\n" );
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document.write( "Let x be the answer.\r\n" );
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document.write( "Make this chart\r\n" );
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document.write( "                  Projects     No. of hours       rate in \r\n" );
document.write( "                  finished      required        projects/hour         \r\n" );
document.write( "Sam alone\r\n" );
document.write( "Peter alone\r\n" );
document.write( "Both together\r\n" );
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document.write( "We put the hours required in each case and 1 for the number of\r\n" );
document.write( "projects completed, which is 1 in all three cases.\r\n" );
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document.write( "                  Projects     No. of hours       rate in \r\n" );
document.write( "                  finished      required        projects/hour         \r\n" );
document.write( "Sam alone            1              7     \r\n" );
document.write( "Peter alone          1              3\r\n" );
document.write( "Both together        1              x\r\n" );
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document.write( "Fill in the rates by dividing projects finished by hours:\r\n" );
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document.write( "                  Projects     No. of hours       rate in \r\n" );
document.write( "                  finished      required        projects/hour         \r\n" );
document.write( "Sam alone            1              7               1/7   \r\n" );
document.write( "Peter alone          1              3               1/3 \r\n" );
document.write( "Both together        1              x               1/x\r\n" );
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document.write( "The equation comes from \r\n" );
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document.write( "                      +  = \r\n" );
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document.write( "                                  +  = \r\n" );
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document.write( "Multilply through by LCD = 21x\r\n" );
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document.write( "                                3x + 7x = 21\r\n" );
document.write( "                                    10x = 21\r\n" );
document.write( "                                      x = 2.1 hours, or 2 hours 6 minutes  \r\n" );
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document.write( "Edwin

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