document.write( "Question 82986This question is from textbook introductory algebra
\n" ); document.write( ": a mechanic requires 2 h to repair a tranmission, whereas an apprentice requires 6 h to make the same repairs. the mechanic worker alone for 1 h and then stopped. how long will it take the apprentice. working alone. to complete the repair? \n" ); document.write( "
Algebra.Com's Answer #59543 by Edwin McCravy(20056)\"\" \"About 
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document.write( "A mechanic requires 2 h to repair a tranmission, whereas an apprentice\r\n" );
document.write( "requires 6 h to make the same repairs. the mechanic worked alone for\r\n" );
document.write( "1 h and then stopped. how long will it take the apprentice. working \r\n" );
document.write( "alone. to complete the repair? \r\n" );
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document.write( "This is a DRT problem, where \"D\" doesn't stand for \"Distance\", but\r\n" );
document.write( "stands for \"DEEDS DONE\", or \"fraction of a deed done\". So make the \r\n" );
document.write( "following chart.  There are four situations to consider:\r\n" );
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document.write( "                                   Deeds     Rate       Time\r\n" );
document.write( "Mechanic doing 1 complete job                                 \r\n" );
document.write( "Apprentice doing 1 complete job                              \r\n" );
document.write( "Mechanic doing partial job                                   \r\n" );
document.write( "Apprentice doing partial job\r\n" );
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document.write( "Let the answer to the question:  \r\n" );
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document.write( ">>...How long will it take the apprentice. working alone. to complete the repair?...<< \r\n" );
document.write( "   \r\n" );
document.write( "be t.  So fill in t for the time for the apprectice to do the partial\r\n" );
document.write( "job of completing the job after the mechanic stops.\r\n" );
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document.write( "                                   Deeds     Rate       Time\r\n" );
document.write( "Mechanic doing 1 complete job                                \r\n" );
document.write( "Apprentice doing 1 complete job                             \r\n" );
document.write( "Mechanic doing partial job                                   \r\n" );
document.write( "Apprentice doing partial job                              t\r\n" );
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document.write( ">>..A mechanic requires 2 h to repair a tranmission..<<\r\n" );
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document.write( "That's 1 deed in 2 hours, so fill in 1 deed and 2 hours on\r\n" );
document.write( "the top row:\r\n" );
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document.write( "                                   Deeds     Rate       Time\r\n" );
document.write( "Mechanic doing 1 complete job        1                    2\r\n" );
document.write( "Apprentice doing 1 complete job                             \r\n" );
document.write( "Mechanic doing partial job                                   \r\n" );
document.write( "Apprentice doing partial job                              t\r\n" );
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document.write( ">>..an apprentice requires 6 h to make the same repairs..<<\r\n" );
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document.write( "That's 1 deed in 6 hours, so fill in 1 deed and 2 hours on\r\n" );
document.write( "the second row:\r\n" );
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document.write( "                                   Deeds     Rate       Time\r\n" );
document.write( "Mechanic doing 1 complete job        1                    2\r\n" );
document.write( "Apprentice doing 1 complete job      1                    6 \r\n" );
document.write( "Mechanic doing partial job                                    \r\n" );
document.write( "Apprentice doing partial job                              t\r\n" );
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document.write( "Next we use the formula R = \"D%2FT\" to fill in the rates\r\n" );
document.write( "on the two top lines:\r\n" );
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document.write( "                                   Deeds     Rate       Time\r\n" );
document.write( "Mechanic doing 1 complete job        1        1/2         2\r\n" );
document.write( "Apprentice doing 1 complete job      1        1/6         6 \r\n" );
document.write( "Mechanic doing partial job                                 \r\n" );
document.write( "Apprentice doing partial job                              t\r\n" );
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document.write( "Now, since the mchanic and the apprentice doing the partial\r\n" );
document.write( "jobs work at the same rates as when they do 1 complete job,\r\n" );
document.write( "we can fill in \"1%2F2\" and \"1%2F6\" for the rates in the bottom two\r\n" );
document.write( "rows:\r\n" );
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document.write( "                                   Deeds     Rate       Time\r\n" );
document.write( "Mechanic doing 1 complete job        1        1/2         2\r\n" );
document.write( "Apprentice doing 1 complete job      1        1/6         6 \r\n" );
document.write( "Mechanic doing partial job                    1/2         1\r\n" );
document.write( "Apprentice doing partial job                  1/6         t\r\n" );
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document.write( "Next we use the formula D = RT to finish filling in the chart:\r\n" );
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document.write( "                                   Deeds     Rate       Time\r\n" );
document.write( "Mechanic doing 1 complete job        1        1/2         2\r\n" );
document.write( "Apprentice doing 1 complete job      1        1/6         6 \r\n" );
document.write( "Mechanic doing partial job          1/2       1/2         1\r\n" );
document.write( "Apprentice doing partial job        t/6       1/6         t\r\n" );
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document.write( "Now that the chart is complete, we form the equation by observing\r\n" );
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document.write( "the partial job which the mechanic did + the partial job which the apprentice\r\n" );
document.write( "did = 1 complete job:\r\n" );
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document.write( "        \r\n" );
document.write( "                            1/2 + t/6 = 1\r\n" );
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document.write( "Can you solve that?  If not post again asking how.\r\n" );
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document.write( "                        Answer: t = 3 hours.\r\n" );
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document.write( "Actually you can check it easy because you can do the whole \r\n" );
document.write( "thing in your head by looking at it this way. The mechanic \r\n" );
document.write( "does a whole job in 2 hours.  So in the one hour he worked, \r\n" );
document.write( "he did half the job. That leave the other half of the job to \r\n" );
document.write( "be done by the apprentice.  The apprentice can do a whole job \r\n" );
document.write( "in 6 hours, so he can do the remaining half-job which the \r\n" );
document.write( "mechanic left him with in half that time, or 3 hours.\r\n" );
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document.write( "Edwin
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