document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194386>Question 1194386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Working together, Jenny and Natalie can assemble a desk in 42/13 hours. Working alone Jenny could have done it in 7 hours. How long would it take Natalie working<BR>\n" );
document.write( "alone?<BR>\n" );
document.write( "hours. </SPAN>\n" );
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document.write( "Let's say this desk has 42 pieces. I'm picking 42 because it will cancel out later on with the other 42 from 42/13.\r<BR>\n" );
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document.write( "Let x be the combined rate of Jenny and Natalie working together. \r<BR>\n" );
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document.write( "The idea is to multiply the number of hours they work together (42/13) with their combined rate (x) and that will tell us how many pieces they're able to assemble (42)\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "(number of hours)*(pieces per hour) = number of pieces<BR>\n" );
document.write( "(42/13)*x = 42<BR>\n" );
document.write( "x = 42*(13/42)<BR>\n" );
document.write( "x = 13\r<BR>\n" );
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document.write( "At this point, it's probably more clear why I picked 42<BR>\n" );
document.write( "The cancellation happens at the last step. \r<BR>\n" );
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document.write( "If there are 42 pieces total, then their combined rate is 13 pieces per hour.\r<BR>\n" );
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document.write( "Another reason why I picked 42 is because it's a multiple of 7.<BR>\n" );
document.write( "If Jenny works alone and she takes 7 hours, then her rate is 42/7 = 6 pieces per hour.<BR>\n" );
document.write( "This leaves Natalie's rate to be 13 - 6 = 7 pieces per hour.\r<BR>\n" );
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document.write( "Therefore, if Natalie works alone, then she will take 42/7 = 6 hours.\r<BR>\n" );
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document.write( "Here's an alternative approach using the standard method to solve rate of work problems.\r<BR>\n" );
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document.write( "n = number of hours Natalie needs if she works alone\r<BR>\n" );
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document.write( "1/n = Natalie's rate in jobs per hour<BR>\n" );
document.write( "In other words, she does 1 job per n hours\r<BR>\n" );
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document.write( "Also, Jenny needs 7 hours, so her rate is 1/7 of a job per hour.\r<BR>\n" );
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document.write( "1/n + 1/7 = their combined rate in jobs per hour<BR>\n" );
document.write( "That simplifies to (7+n)/(7n)\r<BR>\n" );
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document.write( "If they work together and get the job done in 42/13 hours, then their rate must be 13/42 jobs per hour.\r<BR>\n" );
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document.write( "Set this equal to the (7+n)/(7n) and let's solve for n.\r<BR>\n" );
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document.write( "(7+n)/(7n) = 13/42<BR>\n" );
document.write( "42(7+n) = 7n*13<BR>\n" );
document.write( "294+42n = 91n<BR>\n" );
document.write( "91n-42n = 294<BR>\n" );
document.write( "49n = 294<BR>\n" );
document.write( "n = 294/49<BR>\n" );
document.write( "n = 6\r<BR>\n" );
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document.write( "Natalie can get the job done in 6 hours if she works alone.\r<BR>\n" );
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document.write( "Answer: <font color=red>6 hours</font><BR>\n" );
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