document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=334623>Question 334623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The distance between Village A and Village B is 5 miles. A person walks part of the way at 4 mph, then jogs the rest of the way at 9 mph. Find a formula that expresses the total amount of time for the trip, T, as a function of d, the distance walked.\r<BR>\n" );
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document.write( "T(d) = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #239777 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=239777\">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 d\"> represent the distance walked.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5\ -\ d\"> represents the distance jogged.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t_w\"> represent the amount of time spent walking and let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t_j\"> represent the amount of time spent jogging.\r<BR>\n" );
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document.write( "In that we know the walking and jogging speeds and the general relationship <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\ =\ \frac{d}{r}\"> between time, distance, and rate, we can describe the time for each segment of the trip thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t_w\ =\ \frac{d}{4}\">\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 \ \ \ \ \ \ \ \ \ \ t_j\ =\ \frac{5\ -\ d}{9}\">\r<BR>\n" );
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document.write( "The total time is the sum of these two times:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ T\ =\ t_w\ +\ t_j\">\r<BR>\n" );
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document.write( "Substituting to get a function of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ T(d)\ =\ \frac{d}{4}\ +\ \frac{5\ -\ d}{9}\">\r<BR>\n" );
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document.write( "This needs to be simplified by finding the LCD and adding the two fractions.  I'll leave that part in your capable hands.\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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