document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231969>Question 231969</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to write a rational expression for this word problem. Melanie can paint a barn in x days. Her helper Sara can paint the same barn in 2x days. Write a rational expression for the fraction of the barn that they can paint in 1 day by working together. Evaluate the expression for x=5.<BR>\n" );
document.write( "Thanks,<BR>\n" );
document.write( "Jim Koch </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171595 by </B><A HREF=/tutors/aboutme.mpl?userid=Robb><B>Robb(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Robb><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you're evaluating this for x=5, put the 5 in for the x's to give you the following rational expression:\r<BR>\n" );
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document.write( "1/5 + 1/(2*5) = 1/x\r<BR>\n" );
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document.write( "You only want one variable, x.\r<BR>\n" );
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document.write( "So assign x as the part of the barn they can paint together.\r<BR>\n" );
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document.write( "It takes melanie 5 days, so for one days work the fraction is 1/5.\r<BR>\n" );
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document.write( "It takes Sara twice as long, so 10 days.  her work for 1 day is 1/10.\r<BR>\n" );
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document.write( "You don't know how long it will take them working together, so that portion is x\r<BR>\n" );
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document.write( "So you get the following equation:\r<BR>\n" );
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document.write( "1/5 + 1/10 = 1/x\r<BR>\n" );
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document.write( "The LCD is 10x, so multiply everything by 10x to give you:\r<BR>\n" );
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document.write( "2x + x = 10\r<BR>\n" );
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document.write( "Add like terms:\r<BR>\n" );
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document.write( "3x = 10\r<BR>\n" );
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document.write( "Divide both sides by 3:\r<BR>\n" );
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document.write( "x = 3 1/3 days\r<BR>\n" );
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document.write( "So it will take 3 and 1/3 days for them both working together to paint the barn.  \r<BR>\n" );
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document.write( "You can check this by putting 3 1/3 in for x in our equation.\r<BR>\n" );
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document.write( "Hope this helps! </SPAN>\n" );
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