document.write( "Question 1114319: Jonathan and Jose could build a shed, working together, in 6 1/2 hours; but Jonathan worked alone for 3 hours and was then joined by Jose, after which they finished the shed in 5 hours. If they were paid in proportion to what the amount of work each accomplished, how should $96 be divided between them?
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Algebra.Com's Answer #729284 by Edwin McCravy(20055)\"\" \"About 
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document.write( "Suppose Jonathan takes x hours to build 1 shed\r\n" );
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document.write( "Then Jonathan's shed-building rate is 1 shed per x hours.\r\n" );
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document.write( "That's \"matrix%281%2C2%2C1%2Cshed%29%2Fmatrix%281%2C2%2Cx%2Chours%29\" or \"matrix%281%2C2%2C1%2Fx%2Cshed%2Fhour%29\"\r\n" );
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\n" ); document.write( "Jonathan and Jose could build a shed, working together, in 6 1/2 hours;
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document.write( "So their combined shed-building rate is 1 shed per \"6%261%2F2\" hours.\r\n" );
document.write( "That's \"13%2F2\" hours\r\n" );
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document.write( "That's \"matrix%281%2C2%2C1%2Cshed%29%2Fmatrix%281%2C2%2C13%2F2%2Chours%29\" or \"matrix%281%2C2%2C1%2F%2813%2F2%29%2Cshed%2Fhour%29\" or \"matrix%281%2C2%2C2%2F13%2Cshed%2Fhour%29\"\r\n" );
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document.write( "So their combined rate is 2/13:\r\n" );
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\n" ); document.write( "but Jonathan worked alone for 3 hours
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document.write( "So using RATE × TIME = PRODUCTION (IN FRACTION OF A FENCE)\r\n" );
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document.write( "\"%281%2Fx%29%283%29\" = \"3%2Fx\" = Jonathon's production as part of a\r\n" );
document.write( "fence during the first 3 hours.\r\n" );
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document.write( "There was still 1 fence MINUS the part of the fence (3/x) which\r\n" );
document.write( "Jonathon finished during the first 3 hours.  That's the fraction\r\n" );
document.write( " of a fence\r\n" );
document.write( "left to be built.\r\n" );
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\n" ); document.write( "and was then joined by Jose,
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document.write( "Therefore their rate was the combined rate of 2/13 of a fence per hour.\r\n" );
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\n" ); document.write( "after which they finished the shed in 5 hours.
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document.write( "So using RATE × TIME = PRODUCTION (IN FRACTION OF A FENCE)\r\n" );
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document.write( "\"matrix%281%2C3%2C%282%2F13%29%285%29%2C%22%22=%22%22%2C%28x-3%29%2Fx%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C10%2F13%2C%22%22=%22%22%2C%28x-3%29%2Fx%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C10x%2C%22%22=%22%22%2C13%28x-3%29%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C10x%2C%22%22=%22%22%2C13x-39%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2C-3x%2C%22%22=%22%22%2C-39%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2Cx%2C%22%22=%22%22%2C13%29\"\r\n" );
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document.write( "So Jonathon could build a shed by himself in 13 hours,\r\n" );
document.write( "so his shed-building rate is \r\n" );
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document.write( "\"matrix%281%2C2%2C1%2Cshed%29%2Fmatrix%281%2C2%2C13%2Chours%29\" or \"matrix%281%2C2%2C1%2F13%2Cshed%2Fhour%29\" \r\n" );
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document.write( "and since he worked a total of 3+5 or 8 hours, the\r\n" );
document.write( "fraction of the fence Jonathan built was \"8%2F13\" of the fence.\r\n" );
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document.write( "Therefore Jose built the remaining \"5%2F13\" of the fence.\r\n" );
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\n" ); document.write( "If they were paid in proportion to what the amount of work each accomplished, how should $96 be divided between them?
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document.write( "So Jonathon was paid \"8%2F13\" times $96 or $59.08 and\r\n" );
document.write( "Jose was paid \"5%2F13\" times $96 or $36.92.\r\n" );
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document.write( "Edwin
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