document.write( "Question 1026725: I'm stuck on this and need help,....Alfred and Bill working together can paint a house in 24 days. If Alfred can only do 2/3 as much work as Bill, how long would it take each of them to paint the house by themselves? \n" ); document.write( "
Algebra.Com's Answer #641997 by Edwin McCravy(20081)\"\" \"About 
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document.write( "Alfred's rate is 1 house per x days or 1/x house per day.\r\n" );
document.write( "Bill's rate is 1 house per y days or 1/y house per day.\r\n" );
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\n" ); document.write( "If Alfred can only do 2/3 as much work as Bill
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document.write( "So 1/x = (2/3)(1/y)\r\n" );
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document.write( "or 1/x = 2/(3y)\r\n" );
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\n" ); document.write( "Alfred and Bill working together can paint a house in 24 days.
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document.write( "Their combined rate is 1/x + 1/y house per day.\r\n" );
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document.write( "their combined rate times 24 days = 1 house painted. So\r\n" );
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document.write( "(24)(1/x+1/y) = 1 house painted\r\n" );
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document.write( "So we have the system of equations:\r\n" );
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document.write( "\"system%281%2Fx+=+%282%2F3%29%281%2Fy%29%2C%2824%29%281%2Fx%2B1%2Fy%29+=+1%29\"\r\n" );
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document.write( "Simplifying\r\n" );
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document.write( "\"system%281%2Fx+=+2%2F%283y%29%2C1%2Fx%2B1%2Fy+=+1%2F24%29\"\r\n" );
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document.write( "Substitute 2/(3y) for 1/x in the second equation:\r\n" );
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document.write( "\"2%2F%283y%29%2B1%2Fy%29+=+1%2F24%29\"\r\n" );
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document.write( "\"2%2F%283y%29%2B3%2F%283y%29+=+1%2F24%29\"\r\n" );
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document.write( "\"5%2F%283y%29+=+1%2F24%29\"\r\n" );
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document.write( "\"3y=24%2A5\"\r\n" );
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document.write( "Divide both sides by 3\r\n" );
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document.write( "\"y=8%2A5\"\r\n" );
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document.write( "\"y=40\"\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "\"1%2Fx%2B1%2Fy+=+1%2F24\"\r\n" );
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document.write( "\"1%2Fx%2B1%2F40+=+1%2F24\"\r\n" );
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document.write( "Multiply through by LCD = 120\r\n" );
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document.write( "\"120%2B3x+=+5x\"\r\n" );
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document.write( "\"120=2x\"\r\n" );
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document.write( "\"60=x\"\r\n" );
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document.write( "Edwin

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