document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=426006>Question 426006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a man left home driving at 40 miles per hour.when his car broke down, he walked home at a rate of 5 miles per hour;the entire trip (driving and walking) took him 2 1/4 hours. how far from his house did his car break down. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296451 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=296451\">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( "There are two ways to go about this.  The direct way goes right at the quantity we want to determine, but requires more and more difficult calculations.  We'll look at this way first.\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 between home and the breakdown point.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> represent the amount of time spent driving.  And then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2.25\ -\ t\"> must represent the amount of time spent walking.\r<BR>\n" );
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document.write( "We know that distance equals rate times time.  This implies that time is equal to distance divided by rate.\r<BR>\n" );
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document.write( "For the outbound, or driving, part of the trip, we can describe the situation thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{d}{40}\">\r<BR>\n" );
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document.write( "And the return, or walking, part of the trip, the situation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2.25\ -\ t\ =\ \frac{d}{5}\">\r<BR>\n" );
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document.write( "Manipulating the second equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ 2.25\ -\ \frac{d}{5}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{11.25\ -\ d}{5}\">\r<BR>\n" );
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document.write( "Now that we have two expressions that are both equal to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">, set them equal to each other:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{40}\ =\ \frac{11.25\ -\ d}{5}\">\r<BR>\n" );
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document.write( "Now all you have to do is cross-multiply, collect like terms, and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\">, the requested quantity.\r<BR>\n" );
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document.write( "The indirect method is a little simpler on the arithmetic:\r<BR>\n" );
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document.write( "Use distance equals rate times time to create two equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 40t\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 5(2.25\ -\ t)\ =\ 11.25\ -\ 5t\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\ =\ d\">, set the two RHSs equal:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 40t\ =\ 11.25\ -\ 5t\">\r<BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">.  Once you have <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">, multiply times 40 to determine <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\">\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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