document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193839>Question 193839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two kids live 25 kilometers apart. They both leave their houses on bicycles at 9:00a.m.  Kid 1  peddles 15 kilometers per hour, kid 2 peddles 12 kilometers per hour.  What time will they meet?  Please explain and show all steps.\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145524 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=145524\">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( "Considering the term 'kid' actually refers to the offspring of a goat, this is a rather interesting problem indeed.  However, regardless of the actual organisms that are operating the bicycles, the answer is the same.\r<BR>\n" );
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document.write( "Begin with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d = rt\">\r<BR>\n" );
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document.write( "To describe the first one, you would say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d = 15t\">\r<BR>\n" );
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document.write( "Now the distance traveled by the second bicyclist is 25 minus the distance traveled by the first, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25 - d = 12t\">\r<BR>\n" );
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document.write( "Since we are ultimately concerned with the time that they meet, the time they traveled has to be the same for each of them.\r<BR>\n" );
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document.write( "So solve each of the above equations for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t = \frac{d}{15}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t = \frac{25 - d}{12}\"> \r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE t = t\">, we can set these two fractions 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}{15} = \frac{25 - d}{12}\">\r<BR>\n" );
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document.write( "Then cross-multiply:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 12d = 15(25 - d) \ \ \Rightarrow\ \ 12d = 325 - 15d \ \ \Rightarrow\ \ 27d = 325 \ \ \Rightarrow\ \ d = \frac{125}{9}\">\r<BR>\n" );
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document.write( "Which is the distance traveled by the first bicyclist.\r<BR>\n" );
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document.write( "Since the first bicyclist's speed was 15 km/hr, the elapsed time must be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{125}{9}\times\frac{1}{15}=\frac{25}{27}\"> hours.\r<BR>\n" );
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document.write( "Converting that to minutes and seconds to be added to the 9:00 AM start time is left as an exercise for the student.\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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