document.write( "Question 635869: If Angela was to paint her living room alone,it would take her 5 hours. Her sister evenlyn could do the job in 7hours.How long would it take them working together?? \n" ); document.write( "

Algebra.Com's Answer #400605 by Edwin McCravy(20056) $\"\"$ $\"About$

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If Angela was to paint her living room alone, it would take her 5 hours. Her sister evenlyn could do the job in 7hours.How long would it take them working together?\r
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document.write( "Two ways to do it, in your head, or by algebra.\r\n" );
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document.write( "1. In your head:  The LCM of 7 hours and 5 hours is 35 hours.  If they worked\r\n" );
document.write( "together for 35 hours Angela would paint 7 living rooms while Evelyn painted\r\n" );
document.write( "5 living rooms.  So in those 35 hours they would have painted 12 living rooms.\r\n" );
document.write( "So to paint just one living room it would take them 1/12th of 35 hours or\r\n" );
document.write( "35/12ths of an hour.  36 twelfths is 3 hours so 35 twelfths is 1/12 of an hour\r\n" );
document.write( "or 5 minutes less that 3 hours.  Answer: 2 hours and 55 minutes.   \r\n" );
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document.write( "2. By algebra:\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "                        Rooms painted     Time in hours     Rate in rooms/hour\r\n" );
document.write( "Angelo working alone\r\n" );
document.write( "Evelyn working alone\r\n" );
document.write( "Both working together\r\n" );
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document.write( "Let x be the answer, which is the time required for both working together \r\n" );
document.write( "to painr 1 room.  So put x for the rime together and 1 for the number \r\n" );
document.write( "of rooms.\r\n" );
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document.write( "                        Rooms painted     Time in hours     Rate in rooms/hour\r\n" );
document.write( "Angelo working alone\r\n" );
document.write( "Evelyn working alone\r\n" );
document.write( "Both working together         1                  x\r\n" );
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document.write( "Fill in the times for them to paint 1 room :\r\n" );
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document.write( "                        Rooms painted     Time in hours     Rate in rooms/hour\r\n" );
document.write( "Angelo working alone          1                  5 \r\n" );
document.write( "Evelyn working alone          1                  7\r\n" );
document.write( "Both working together         1                  x\r\n" );
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document.write( "Fill in the rate in rooms/hour by dividing the number of rooms by the number\r\n" );
document.write( "of hours.\r\n" );
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document.write( "                        Rooms painted     Time in hours     Rate in rooms/hour\r\n" );
document.write( "Angelo working alone          1                  5                 1/5 \r\n" );
document.write( "Evelyn working alone          1                  7                 1/7\r\n" );
document.write( "Both working 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( "Multioply by 35x\r\n" );
document.write( "                         7x + 5x = 35\r\n" );
document.write( "                             12x = 35\r\n" );
document.write( "                               x = \r\n" );
document.write( "                               x =  hours or \r\n" );
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document.write( "                        2 hours and 55 minutes.\r\n" );
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document.write( "Edwin

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