document.write( "Question 387867: If Michael can paint a house in 8 hours and a Samantha can paint a house in 2 hours, how long will it take them together? \n" ); document.write( "
Algebra.Com's Answer #274207 by Edwin McCravy(20055)\"\" \"About 
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If Michael can paint a house in 8 hours and a Samantha can paint a house in 2
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document.write( "You can do it in your head without algebra, but you're probably supposed\r\n" );
document.write( "to do it by algebra, so we''l do it both ways.  First, in your head:\r\n" );
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document.write( "In the 8 hours Michael takes to paint only one house, Samantha will have\r\n" );
document.write( "painted 4 houses.  So in 8 hours together they will have painted 5 houses. So\r\n" );
document.write( "it'll only take them 1/5th of 8 hours to paint just one house, and 1/5 of 8 is\r\n" );
document.write( "8/5 hours.  That's 1 3/5 hours or 1 hour and 36 minutes.\r\n" );
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document.write( "Now we do it using algebra:\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "             Houses painted     Time in hours   Rate in houses/hour\r\n" );
document.write( "Michael\r\n" );
document.write( "Samantha\r\n" );
document.write( "Together\r\n" );
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document.write( "Let x be the time it takes them to paint 1 house working together, so\r\n" );
document.write( "fill in 1 for the number of houses, and x for the time.\r\n" );
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document.write( "             Houses painted     Time in hours   Rate in houses/hour\r\n" );
document.write( "Michael\r\n" );
document.write( "Samantha\r\n" );
document.write( "Together           1                  x\r\n" );
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document.write( ">>...Michael can paint ONE house in 8 hours...<<\r\n" );
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document.write( "So we fill in 1 for his number of houses painted and 8 for his time:\r\n" );
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document.write( "             Houses painted     Time in hours   Rate in houses/hour\r\n" );
document.write( "Michael            1                  8               1/8\r\n" );
document.write( "Samantha                              \r\n" );
document.write( "Together           1                  x               1/x\r\n" );
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document.write( ">>...Samantha can paint a house in 2 hours...<<\r\n" );
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document.write( "So we fill in 1 for her number of houses painted and 2 for her time:\r\n" );
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document.write( "             Houses painted     Time in hours   Rate in houses/hour\r\n" );
document.write( "Michael            1                  8\r\n" );
document.write( "Samantha           1                  2 \r\n" );
document.write( "Together           1                  x\r\n" );
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document.write( "Now we fill the rate in houses/hour by dividing houses painted by hours\r\n" );
document.write( "in all three cases:\r\n" );
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document.write( "             Houses painted     Time in hours   Rate in houses/hour\r\n" );
document.write( "Michael            1                  8                 1/8 \r\n" );
document.write( "Samantha           1                  2                 1/2\r\n" );
document.write( "Together           1                  x                 1/x \r\n" );
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document.write( "Now we form our equation from the rates:\r\n" );
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document.write( "        Michael's rate + Samantha's rate = their rate together\r\n" );
document.write( "              1/8      +      1/2        =        1/x\r\n" );
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document.write( "Multiply through by the LCD of 8x\r\n" );
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document.write( "                                  x + 4x = 8\r\n" );
document.write( "                                      5x = 8\r\n" );
document.write( "                                       x = 8/5\r\n" );
document.write( "                                       x = 1 3/5 hours or 1 hour 36 minutes.\r\n" );
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document.write( "Edwin
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