document.write( "Question 1013758: Max can finish repairing a machine in 4 hours. His helper can do the same job in 8 hours. Max began the job alone and work for 2 hours.His helper joined until the was completed. How long did it take them to finish the job?
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Algebra.Com's Answer #630049 by Edwin McCravy(20060)\"\" \"About 
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document.write( "That answer above 1 hour 40 minutes is incorrect, although the 4/3 hours\r\n" );
document.write( "is correct.\r\n" );
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\n" ); document.write( "Max can finish repairing a machine in 4 hours.
\n" ); document.write( "His helper can do the same job in 8 hours. Max began the job alone
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document.write( "Let the answer be x.  Make this chart and put x in the middle column\r\n" );
document.write( "on the 4th row,\r\n" );
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document.write( "                            fraction\r\n" );
document.write( "                               of\r\n" );
document.write( "                              jobs     time      rate in\r\n" );
document.write( "                              done    in hrs     jobs/hr\r\n" );
document.write( "Max alone doing 1 job         \r\n" );
document.write( "Helper alone doing 1 job   \r\n" );
document.write( "Max alone for 2 hours\r\n" );
document.write( "Both together for x hours               x\r\n" );
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document.write( "Max can finish repairing a machine in 4 hours. \r\n" );
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document.write( "So he can do 1 job in 4 hours so we fill in the first two blanks\r\n" );
document.write( "in the first row:\r\n" );
document.write( "\r\n" );
document.write( "                            fraction\r\n" );
document.write( "                               of\r\n" );
document.write( "                              jobs     time      rate in\r\n" );
document.write( "                              done    in hrs     jobs/hr\r\n" );
document.write( "Max alone doing 1 job          1        4 \r\n" );
document.write( "Helper alone doing 1 job   \r\n" );
document.write( "Max alone for 2 hours\r\n" );
document.write( "Both together for x hours               x\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
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document.write( "His helper can do the same job in 8 hours. \r\n" );
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document.write( "So the helper can do 1 job in 8 hours so we fill in the first two blanks\r\n" );
document.write( "in the second row:\r\n" );
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document.write( "                            fraction\r\n" );
document.write( "                               of\r\n" );
document.write( "                              jobs     time      rate in\r\n" );
document.write( "                              done    in hrs     jobs/hr\r\n" );
document.write( "Max alone doing 1 job          1        4 \r\n" );
document.write( "Helper alone doing 1 job       1        8  \r\n" );
document.write( "Max alone for 2 hours\r\n" );
document.write( "Both together for x hours               x\r\n" );
document.write( " \r\n" );
document.write( "Next we fill in the rates in the first two rows by dividing the\r\n" );
document.write( "jobs done by the time in hours.\r\n" );
document.write( "\r\n" );
document.write( "                            fraction\r\n" );
document.write( "                               of\r\n" );
document.write( "                              jobs     time      rate in\r\n" );
document.write( "                              done    in hrs     jobs/hr\r\n" );
document.write( "Max alone doing 1 job          1        4           1/4\r\n" );
document.write( "Helper alone doing 1 job       1        8           1/8\r\n" );
document.write( "Max alone for 2 hours                   \r\n" );
document.write( "Both together for x hours               x\r\n" );
document.write( "\r\n" );
document.write( "Max began the job alone and work for 2 hours.\r\n" );
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document.write( "Max's rate for those 2 hours is the same as when doing 1 job, \r\n" );
document.write( "namely 1/4, so we put 2 for the hours in the 3rd row and 1/4 for the rate \r\n" );
document.write( "\r\n" );
document.write( "                            fraction\r\n" );
document.write( "                               of\r\n" );
document.write( "                              jobs     time      rate in\r\n" );
document.write( "                              done    in hrs     jobs/hr\r\n" );
document.write( "Max alone doing 1 job          1        4           1/4\r\n" );
document.write( "Helper alone doing 1 job       1        8           1/8\r\n" );
document.write( "Max alone for 2 hours                   2           1/4\r\n" );
document.write( "Both together for x hours               x\r\n" );
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document.write( "We fill in the number of jobs done by multiplying the rate by\r\n" );
document.write( "the time (1/4)(2) = 1/2, which is half a job, so we fill 1/2\r\n" );
document.write( "in the 1st column on the 3rd row:\r\n" );
document.write( "\r\n" );
document.write( "                            fraction\r\n" );
document.write( "                               of\r\n" );
document.write( "                              job      time      rate in\r\n" );
document.write( "                              done    in hrs     jobs/hr\r\n" );
document.write( "Max alone doing 1 job          1        4           1/4\r\n" );
document.write( "Helper alone doing 1 job       1        8           1/8\r\n" );
document.write( "Max alone for 2 hours         1/2       2           1/4\r\n" );
document.write( "Both together for x hours               x \r\n" );
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document.write( "His helper joined until the was completed. \r\n" );
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document.write( "Their combined rate is the sum of their rates, 1/4+1/8 = 2/8+1/8 = 3/8\r\n" );
document.write( "So we fill that in the last column on the 4th row:\r\n" );
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document.write( "                            fraction\r\n" );
document.write( "                               of\r\n" );
document.write( "                              job      time      rate in\r\n" );
document.write( "                              done    in hrs     jobs/hr\r\n" );
document.write( "Max alone doing 1 job          1        4           1/4\r\n" );
document.write( "Helper alone doing 1 job       1        8           1/8\r\n" );
document.write( "Max alone for 2 hours         1/2       2           1/4\r\n" );
document.write( "Both together for x hours               x           3/8\r\n" );
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document.write( "We fill in the number of jobs done in the x hours by multiplying the \r\n" );
document.write( "rate by the time (3/8)x, so we fill 1/2 in the 1st column on the 4th row:\r\n" );
document.write( "\r\n" );
document.write( "                            fraction\r\n" );
document.write( "                               of\r\n" );
document.write( "                              jobs     time      rate in\r\n" );
document.write( "                              done    in hrs     jobs/hr\r\n" );
document.write( "Max alone doing 1 job          1        4           1/4\r\n" );
document.write( "Helper alone doing 1 job       1        8           1/8\r\n" );
document.write( "Max alone for 2 hours         1/2       2           1/4\r\n" );
document.write( "Both together for x hours   (3/8)x      x           3/8\r\n" );
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document.write( "How long did it take them to finish the job?\r\n" );
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document.write( "The sum of the fractions of a job done in the 2 hours plus the fraction\r\n" );
document.write( "of the job done in the x hours must total up to 1 job, so\r\n" );
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document.write( "                       1/2 + (3/8)x = 1\r\n" );
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document.write( "Multiply through by LCD = 8\r\n" );
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document.write( "                          4 + 3x = 8\r\n" );
document.write( "                              3x = 4\r\n" );
document.write( "                               x = 4/3 = 1 1/3 hours = 1 hour 20 minutes\r\n" );
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document.write( "Edwin
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