document.write( "Question 264387: Bart can complete his science task twice as quickly as Carl can. When they Work together, the task takes 3 hours. How long would it take Carl to do the work alone? \n" ); document.write( "
Algebra.Com's Answer #194645 by Edwin McCravy(20056)\"\" \"About 
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Bart can complete his science task twice as quickly as Carl can. When they Work together, the task takes 3 hours. How long would it take Carl to do the work alone?
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document.write( "Make this chart\r\n" );
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document.write( "                NUMBER OF TASKS       RATE       TIME\r\n" );
document.write( "Bart                 \r\n" );
document.write( "Carl                               \r\n" );
document.write( "Both together        \r\n" );
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document.write( "In all three cases, Bart alone, Carl alone, and both together,\r\n" );
document.write( "they will all do just 1 task so we put 1 for the NUMBER OF TASKS\r\n" );
document.write( "in each of the three cases \r\n" );
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document.write( "                NUMBER OF TASKS       RATE       TIME\r\n" );
document.write( "Bart                  1               \r\n" );
document.write( "Carl                  1                               \r\n" );
document.write( "Both together         1              \r\n" );
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document.write( "The question asks:\r\n" );
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\n" ); document.write( ">>...How long would it take Carl to do the work alone?...<<
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document.write( "So we put x for Carl's time:\r\n" );
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document.write( "                NUMBER OF TASKS       RATE       TIME\r\n" );
document.write( "Bart                  1                           \r\n" );
document.write( "Carl                  1                           x                \r\n" );
document.write( "Both together         1               \r\n" );
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\n" ); document.write( ">>...Bart can complete his science task twice as quickly as Carl can...<<
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document.write( "That means Bart requires only HALF as much time, so we divide\r\n" );
document.write( "Carl's by 2 to get Bart's time.  So we put x/2 for Bart's time.\r\n" );
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document.write( "                NUMBER OF TASKS       RATE       TIME\r\n" );
document.write( "Bart                  1                          x/2\r\n" );
document.write( "Carl                  1                           x                \r\n" );
document.write( "Both together         1                         \r\n" );
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\n" ); document.write( ">>...When they work together, the task takes 3 hours...<<
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document.write( "So we put 3 for the time for \"both together\"\":\r\n" );
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document.write( "                NUMBER OF TASKS       RATE       TIME\r\n" );
document.write( "Bart                  1                          x/2\r\n" );
document.write( "Carl                  1                           x                \r\n" );
document.write( "Both together         1                           3\r\n" );
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document.write( "Now we figure the three rates in tasks per hour.\r\n" );
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document.write( "\"RATE+=+%22NUMBER_OF_TASKS%22%2FTIME\"\r\n" );
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document.write( "Bart's rate = \"1\"\"%22%F7%22\"\"x%2F2\"\"%22%22=1%22%22\"\"%22%2A%22\"\"2%2Fx=2%2Fx\"\r\n" );
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document.write( "Carl's rate = \"1%2Fx\"\r\n" );
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document.write( "\"Both together\" rate = \"1%2F3\"\r\n" );
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document.write( "So fill those in:\r\n" );
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document.write( "                NUMBER OF TASKS       RATE       TIME\r\n" );
document.write( "Bart                  1               2/x        x/2\r\n" );
document.write( "Carl                  1               1/x         x                \r\n" );
document.write( "Both together         1               1/3         3\r\n" );
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document.write( "Now we get the equation from the rates:\r\n" );
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document.write( "Bart's RATE + Carl's RATE = the RATE for \"both together\":\r\n" );
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document.write( "         \"2%2Fx+%2B+1%2Fx+=+1%2F3\"\r\n" );
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document.write( "Get a common denominator of \"3x\"  and multiply\r\n" );
document.write( "every term by \"3x\"\r\n" );
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document.write( "         \"%283x%29%282%2Fx%29+%2B+%283x%29%281%2Fx%29+=+%283x%29%281%2F3%29\"\r\n" );
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document.write( "         \r\n" );
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document.write( "         \"6+%2B+3+=+x\"\r\n" );
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document.write( "         \"9=x\"\r\n" );
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document.write( "So it would take Carl 9 hours to complete the task.\r\n" );
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document.write( "Edwin
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