document.write( "Question 974568: Sumi can wash windows of an office building in 3/4 the time it takes her apprentice. One day they worked on the building together for 2h 16 min then Sumi continued alone. It took 4 h 32 min more to complete the job. How long would it take her apprentice to wash all the windows?\r
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Algebra.Com's Answer #596450 by Edwin McCravy(20056)\"\" \"About 
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Sumi can wash windows of an office building in 3/4 the time it takes her
\n" ); document.write( "apprentice. One day they worked on the building together for 2h 16 min then Sumi
\n" ); document.write( "continued alone. It took 4 h 32 min more to complete the job. How long would it
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document.write( "Let x hours represent the solution, how long it would take the apprentice to\r\n" );
document.write( "wash all the windows\r\n" );
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document.write( "So the apprentice's window-washing rate is 1 set of windows per x hours.\r\n" );
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document.write( "That is to say that the apprentice's window-washing rate is \"matrix%281%2C4%2C1%2Cset%2Cof%2Cwindows%29%2Fmatrix%281%2C2%2Cx%2Chours%29\" or \"matrix%281%2C2%2C+1%2Fx%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29\"\r\n" );
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\n" ); document.write( " Sumi can wash windows of an office building in 3/4 the time it takes her apprentice.
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document.write( "Then Sumi's window-washing rate is 1 set of windows per \"expr%283%2F4%29x\" hours.\r\n" );
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document.write( "Therefore Sumi's window-washing rate is \"matrix%281%2C4%2C1%2Cset%2Cof%2Cwindows%29%2Fmatrix%281%2C2%2Cexpr%283%2F4%29x%2Chours%29\" or \"matrix%281%2C2%2C+1%2Fexpr%283%2F4%29x%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29\"\r\n" );
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document.write( "We simplify \"1%2Fexpr%283%2F4%29x\"by multiplying top and bottom by 4 getting\r\n" );
document.write( "\"4%2F%283x%29\". So Sumi's window-washing rate is\r\n" );
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document.write( "\"matrix%281%2C2%2C+4%2F%283x%29%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29\"\r\n" );
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\n" ); document.write( "One day they worked on the building together...
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document.write( "So their combined rate was the sum of those rates\r\n" );
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document.write( "\"matrix%281%2C2%2C+1%2Fx%2B4%2F%283x%29%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29\"\r\n" );
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document.write( "We simplify \"1%2Fx%2B4%2F%283x%29=3%2F%283x%29%2B4%2F%283x%29=7%2F%283x%29\"\r\n" );
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document.write( "So their combined rate was:\r\n" );
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document.write( "\"matrix%281%2C2%2C+7%2F%283x%29%2C+matrix%281%2C3%2Cset%2Cof%2Cwindows%29%2Fhr%29%29\"\r\n" );
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\n" ); document.write( "One day they worked on the building together for 2h 16 min
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document.write( "We convert that to an improper fraction of hours.\r\n" );
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document.write( "Since rate×time = production, during that time the fraction of \r\n" );
document.write( "the set of windows they washed working together was\r\n" );
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document.write( "\"%287%2F%283x%29%29%2A%2834%2F15%29\"\"%22%22=%22%22\"\"matrix%281%2C6%2C238%2F%2845x%29%2Cof%2Cthe%2Cset%2Cof%2Cwindows%29\"\r\n" );
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document.write( "then Sumi continued alone. It took 4 h 32 min more to complete the job.\r\n" );
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document.write( "We convert that to an improper fraction of hours.\r\n" );
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document.write( "Again, since rate×time = production, during that time the fraction of \r\n" );
document.write( "the set of windows that Sumi washed working alone was\r\n" );
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document.write( "\"%284%2F%283x%29%29%2A%2868%2F15%29\"\"%22%22=%22%22\"\"matrix%281%2C6%2C272%2F%2845x%29%2Cof%2Cthe%2Cset%2Cof%2Cwindows%29\"\r\n" );
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document.write( "The equation comes from\r\n" );
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document.write( "\"%22%22%2B%22%22\"\"%22%22=%22%22\"\"%28matrix%285%2C1%2C%0D%0A%0D%0A1%2Ccomplete%2Cset%2Cof%2C+windows%29%29\"\r\n" );
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document.write( "Multiply through by 45x\r\n" );
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document.write( "\"238%2B272\"\"%22%22=%22%22\"\"45x\"\r\n" );
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document.write( "\"510\"\"%22%22=%22%22\"\"45x\"\r\n" );
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document.write( "\"510%2F45\"\"%22%22=%22%22\"\"x\"\r\n" );
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document.write( "\"34%2F3\"\"%22%22=%22%22\"\"x\"\r\n" );
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document.write( "\"11%261%2F3\"\"%22%22=%22%22\"\"x\"\r\n" );
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document.write( "That's 11 hours 20 minutes, so that's how long it would take\r\n" );
document.write( "the apprentice working alone to wash all the windows.\r\n" );
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document.write( "Edwin
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