document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181560>Question 181560</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry  Structure and Method </A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The county's new asphalt paving machine can surface 1km of highway in 10 hours.  A mcuh older machine can surface 1km in 18 hours.  How long will it take them to surface 21km of highway if they start at opposite ends and work day and night? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136159 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "This method works for all sorts of shared work problems.  Painting rooms, pumping water in and out of a tank, mowing lawns, etc.\r<BR>\n" );
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document.write( "If <i>A</i> can do an entire job in <i>x</i> time periods, then <i>A</i> can do <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac {1}{x}\"> of the job in 1 time period.\r<BR>\n" );
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document.write( "Likewise, if <i>B</i> can do an entire job in <i>y</i> time periods, then <i>B</i> can do <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac {1}{y} \"> of the job in 1 time period.\r<BR>\n" );
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document.write( "Together, <i>A</i> and <i>B</i> can do <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac {1}{x} + \frac {1}{y}\"> of the job in 1 time period.\r<BR>\n" );
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document.write( "Therefore, <i>A</i> and <i>B</i> can do the entire job in\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac {1}{\frac {1}{x} + \frac {1}{y}} = \frac {1}{\frac{x + y}{xy}} = \frac {xy}{x + y}\">\r<BR>\n" );
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document.write( "time periods.\r<BR>\n" );
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document.write( "For your problem, <i>A</i> and <i>B</i> are the new machine and the old machine, <i>x</i> and <i>y</i> are 10 hours and 18 hours, your time period is 1 hour and 1 entire job is paving 1 km of roadway.\r<BR>\n" );
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document.write( "So take the results of the calculations outlined above which will be the number of hours for both machines to pave 1 km (leave it expressed as an improper fraction) and multiply by 21 to get the total hours required for the entire 21 km stretch of highway.\r<BR>\n" );
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document.write( "<i><b>Super Double Plus Extra Credit:</b></i> How would the formula derived above change if you considered three entities working together at three different rates?\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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