document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237997>Question 237997</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On a 135 mile bicycle excursion, Maria averaged 5 miles per hour slower during the last 75 miles than for the first 60 miles. The entire trip took 8 hours. Find her rate for the first 60 miles. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174921 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=174921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> represent the rate during the 60 mile leg.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\ -\ 5\"> is the rate for the 75 mile leg.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> represent the time to complete the 60 mile leg.  Then the time to complete the 75 mile leg must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 8\ -\ t\">\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{60}{r}\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8\ -\ t\ =\ \frac{75}{r\ -\ 5}\">\r<BR>\n" );
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document.write( "Solve the second equation for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> (left as an exercise for the student).  Now you will have two expressions equal to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">.  Set them equal and simplify.  The result will be the following quadratic equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8r^2\ -\ 175r\ -\ 300\ =\ 0\">\r<BR>\n" );
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document.write( "Factor and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\">.  You will obtain two positive roots, but one of them will be < 5, and can be excluded because that would make <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r - 5 < 0\"> meaning she went backwards during the 75 mile leg.\r<BR>\n" );
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document.write( " <BR>\n" );
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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