document.write( "Question 120244: A machine can produce a certain number of pages twice as fast as another
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Algebra.Com's Answer #88130 by Edwin McCravy(20060)\"\" \"About 
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A machine can produce a certain number of pages twice as fast as another
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document.write( "Make this chart:\r\n" );
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document.write( "              No. of Pages      Rate in pages/min       Time\r\n" );
document.write( "Fast machine                                                              \r\n" );
document.write( "Slow machine                                               \r\n" );
document.write( "Both together                                             \r\n" );
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document.write( "Let N = the number of pages.\r\n" );
document.write( "Let x = the number of minutes it takes the fast machine to\r\n" );
document.write( "       produce N pages,\r\n" );
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document.write( "Fill those in:\r\n" );
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document.write( "              No. of Pages      Rate in pages/min       Time\r\n" );
document.write( "Fast machine       N                                     x                \r\n" );
document.write( "Slow machine       N                                        \r\n" );
document.write( "Both together      N                                         \r\n" );
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document.write( "We read:\r\n" );
document.write( ">>...Operating together these machines can produce this number \r\n" );
document.write( "of pages in 8 minutes...<<\r\n" );
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document.write( "So we fill in the 8:\r\n" );
document.write( "              No. of Pages      Rate in pages/min       Time\r\n" );
document.write( "Fast machine       N                                     x                \r\n" );
document.write( "Slow machine       N                                      \r\n" );
document.write( "Both together      N                                     8 \r\n" );
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document.write( "We read:\r\n" );
document.write( ">>...A machine can produce a certain number of pages twice as \r\n" );
document.write( "fast as another machine...<<\r\n" );
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document.write( "So the slow machine takes twice as long as the fast machine, so\r\n" );
document.write( "fill in twice x or 2x for the slow machine's time:\r\n" );
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document.write( "              No. of Pages      Rate in pages/min       Time\r\n" );
document.write( "Fast machine       N                                     x                \r\n" );
document.write( "Slow machine       N                                    2x\r\n" );
document.write( "Both together      N                                     8 \r\n" );
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document.write( "Now we get the three rates in pages/minute by dividing the number\r\n" );
document.write( "of pages by the number or minutes, that is, \r\n" );
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document.write( "                        Rate = (No. of pages)/Time:\r\n" );
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document.write( "              No. of Pages      Rate in pages/min       Time\r\n" );
document.write( "Fast machine       N                  \"N%2Fx\"                x                \r\n" );
document.write( "Slow machine       N                 \"N%2F%282x%29\"              2x\r\n" );
document.write( "Both together      N                  \"N%2F8\"                8 \r\n" );
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document.write( "So to get the equation we use this idea:\r\n" );
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document.write( "Rate of 1st + Rate of 2nd = Their rate together\r\n" );
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document.write( "\"N%2Fx\" + \"N%2F%282x%29\" = \"N%2F8\"\r\n" );
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document.write( "Multiply thru by LCD = \"8x\" written as \"%28%288x%29%2F1%29\"\r\n" );
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document.write( "\"%28%288x%29%2F1%29\"\"N%2Fx\" + \"%28%288x%29%2F1%29\"\"N%2F%282x%29\" = \"%28%288x%29%2F1%29\"\"N%2F8\"\r\n" );
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document.write( "Cancel the x's in the first term, the 2 into the 8, \r\n" );
document.write( "leaving 4 in the second term, also cancel the x's in \r\n" );
document.write( "the second term. Cancel the 8's in the term on the\r\n" );
document.write( "right:\r\n" );
document.write( "               4\r\n" );
document.write( "\"%28%288cross%28x%29%29%2F1%29\"\"N%2Fcross%28x%29\" + \"%28%28cross%288%29cross%28x%29%29%2F1%29\"\"N%2F%28cross%282%29cross%28x%29%29\" = \"%28%28cross%288%29x%29%2F1%29\"\"N%2Fcross%288%29\"\r\n" );
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document.write( "So we have\r\n" );
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document.write( "8N + 4N = xN\r\n" );
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document.write( "    12N = xN\r\n" );
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document.write( "Divide both sides by N\r\n" );
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document.write( "     12 = x\r\n" );
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document.write( "So the fast machine's time is x = 12 minutes. \r\n" );
document.write( "Then the slow machine's time is 2x = 24 minutes.\r\n" );
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document.write( "Edwin

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