document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207777>Question 207777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three girls, Laura, Tammy, and Jeri can do the chores in 1 hour and 20 minutes. If Jeri did all the chores she would take twice as long as Tammy and 4 hours longer than Laura. How long would each girl take to do the chores alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157182 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> well i must say you picked a good one.<BR>\n" );
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document.write( "here's how i think i solved it.<BR>\n" );
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document.write( "the problem:<BR>\n" );
document.write( "Three girls, Laura, Tammy, and Jeri can do the chores in 1 hour and 20 minutes. If Jeri did all the chores she would take twice as long as Tammy and 4 hours longer than Laura. How long would each girl take to do the chores alone?<BR>\n" );
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document.write( "let J = jeri's rate of work <BR>\n" );
document.write( "let T = Tammy's rate of work<BR>\n" );
document.write( "let L = Laura's rate of work<BR>\n" );
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document.write( "General Formula is RT = U which means that Rate * Time = Units produced<BR>\n" );
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document.write( "The Units produced = 1 Set of Chores<BR>\n" );
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document.write( "The Time it took for all 3 girls working at the same time = 1 and 1/3 hours = 4/3 hours = 1.3333...<BR>\n" );
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document.write( "Your formula for when all 3 girls are working is:<BR>\n" );
document.write( "4/3 * (J + T + L) = 1<BR>\n" );
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document.write( "You say that Jeri takes twice as long as Tammy to do the chores working alone.<BR>\n" );
document.write( "This means that if Jeri takes h hours, Tammy only takes h/2 hours because h is 2 times h/2<BR>\n" );
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document.write( "J*h = 1 means that J = 1/h<BR>\n" );
document.write( "T*(h/2) = 1 means that T = 2/h<BR>\n" );
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document.write( "You say that Jeri takes 4 hours longer than Laura.<BR>\n" );
document.write( "This means that if Jeri takes h hours, Laura must take (h-4) hours.<BR>\n" );
document.write( "L * (h-4) = 1 means that L = 1/(h-4)<BR>\n" );
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document.write( "you can now substitute 1/h for J and 2/h for T and 1/(h-4) for L in the original equation of 4/3 * (J + T + L) = 1<BR>\n" );
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document.write( "your original equation becomes:<BR>\n" );
document.write( "4/3 * ((1/h) + (2/h + 1/(h-4)) = 1<BR>\n" );
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document.write( "if you multiply both sides of this equation by h*(h-4) you will be able to remove all the denominators.<BR>\n" );
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document.write( "your equation becomes:<BR>\n" );
document.write( "4/3 * ((h-4) + 2*(h-4) + h) = h*(h-4)<BR>\n" );
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document.write( "this reduces to:<BR>\n" );
document.write( "4/3 * (4h-12) = h^2 - 4h<BR>\n" );
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document.write( "when you multiply both sides by 3 this becomes:<BR>\n" );
document.write( "3h^2 - 28h + 48 = 0<BR>\n" );
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document.write( "when you solve this using the quadratic formula, your answers become:<BR>\n" );
document.write( "h = 7.070367517<BR>\n" );
document.write( "or<BR>\n" );
document.write( "h = 2.262965816<BR>\n" );
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document.write( "h = 2.2... is rejected because h-4 would become negative.<BR>\n" );
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document.write( "your answer becomes h = 7.070367517<BR>\n" );
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document.write( "substituting this value into the equation of 3h^2 - 28h + 48 = 0 makes 0 = 0 showing that this is a legitimate root of that equation.<BR>\n" );
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document.write( "substituting this value into the equation of 4/3 * ((1/h) + (2/h + 1/(h-4)) = 1 makes 1 = 1 showing that this is a legitimate solution to the original equation.<BR>\n" );
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document.write( "J's rate is 1/h = 1/7.070367517 units per hour.<BR>\n" );
document.write( "T's rate is 2/h = 2/7.070367517 units per hour.<BR>\n" );
document.write( "L's rate is 1/(h-4) = 1/3.070567517 units per hour.<BR>\n" );
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document.write( "it takes J (1/h)*x hours to complete the chores.<BR>\n" );
document.write( "this means that (1/h)*x = 1 which means that x = 1/(1/h) = h<BR>\n" );
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document.write( "it takes T (2/h)*y hours to complete the chores.<BR>\n" );
document.write( "this means that (2/h)*y = 1 which means that y = 1/(2/h) = h/2<BR>\n" );
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document.write( "it takes L (1/(h-4)*z hours to complete the chores.<BR>\n" );
document.write( "this means that (1/(h-4))*z = 1 which means that z = 1/(1/(h-4)) = (h-4)<BR>\n" );
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document.write( "everything checks out.<BR>\n" );
document.write( "J takes twice as long as T to complete the chores.<BR>\n" );
document.write( "J takes 4 hours more than L to complete the chores.<BR>\n" );
document.write( "adding up all their rates when they work together produces 1 set of chores.<BR>\n" );
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document.write( " </SPAN>\n" );
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