document.write( "Question 906517: It takes Ralph 5 hours to paint a fence alone. Lisa can do the same job in 10 hours. If Ralph paints alone for 45 minutes before Lisa begins helping, how long must they work together to finish painting the fence? Give your answer as a simplified fraction. \n" ); document.write( "
Algebra.Com's Answer #550126 by Edwin McCravy(20054)\"\" \"About 
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It takes Ralph 5 hours to paint a fence alone.
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document.write( "So, Ralph's painting rate is 1 fence per 5 hours or \"matrix%281%2C2%2C1%2Cfence%29%2Fmatrix%281%2C2%2C5%2Chours%29\" or \"matrix%281%2C2%2C1%2F5%2Cfence%2Fhour%29\" \r\n" );
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\n" ); document.write( "Lisa can do the same job in 10 hours.
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document.write( "So, Lisa's painting rate is 1 fence per 10 hours or \"matrix%281%2C2%2C1%2Cfence%29%2Fmatrix%281%2C2%2C10%2Chours%29\" or \"matrix%281%2C2%2C1%2F10%2Cfence%2Fhour%29\"\r\n" );
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\n" ); document.write( "If Ralph paints alone for 45 minutes...
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document.write( "That's \"3%2F4\"ths of an hour. so his rate times his time is\r\n" );
document.write( "\"%28matrix%281%2C2%2C1%2F5%2Cfence%2Fhour%29%29%2A%28matrix%281%2C2%2C3%2F4%2Chour%29%29\"\"%22%22=%22%22\"\"%22%22=%22%22\"\"matrix%281%2C2%2C3%2F20%2Cfence%29\"\r\n" );
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document.write( "So Ralph has painted only \"3%2F20\"ths of a fence, and so thete is\r\n" );
document.write( "\"1-17%2F20=20%2F20-3%2F20=17%2F20\"ths of the fence left to paint.\r\n" );
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\n" ); document.write( "...before Lisa begins helping,
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document.write( "Now their combined rate then is the sum of their individual rates: \"matrix%281%2C2%2C1%2F5%2B1%2F10=2%2F10%2B1%2F10=3%2F10%2Cfence%2Fhour%29\"\r\n" );
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\n" ); document.write( "how long must they work together to finish painting the fence?
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document.write( "Let the number of hours be x.  Then during those x hours they\r\n" );
document.write( "paint the remaining \"17%2F20\"ths of the fence:\r\n" );
document.write( "\"matrix%281%2C2%2C3%2F10%2Cfence%2Fhour%29%2Amatrix%281%2C2%2C%22%28x%22%2C%22hours%29%22%29\"\"%22%22=%22%22\"\"matrix%281%2C2%2C17%2F20%2Cfence%29\" \r\n" );
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document.write( "\"expr%283%2F10%29x=17%2F20\"\r\n" );
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document.write( "Multiply both sides by 20\r\n" );
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document.write( "\"20%2Aexpr%283%2F10%29x=20%2Aexpr%2817%2F20%29\"\r\n" );
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document.write( "\"6x=17\"\r\n" );
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document.write( "\"x=17%2F6=2%265%2F6\"hours or 2 hours 50 minutes.\r\n" );
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document.write( "Edwin
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