document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129835>Question 129835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two towns are 243 miles apart.  Bob and Joe each start in on of the towns at 12:00 PM and drive towards each other with uniform motion.  Bob drives 45mph, joe drives 65 mph.  When do they meet (at what time)?  WHERE do they meet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94806 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=94806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=d%2Fr ALIGN=MIDDLE  ALT=\"t=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since we are interested in when and where they meet, their drive times must be equal.\r<BR>\n" );
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document.write( "Let's say that x is the distance Bob drives at 45 mph.  That means that the distance Joe drives at 65 mph is 243 - x.\r<BR>\n" );
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document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=d%2Fr ALIGN=MIDDLE  ALT=\"t=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Bob's drive time is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=x%2F45 ALIGN=MIDDLE  ALT=\"t=x%2F45\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and Joe's drive time is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28243-x%29%2F65 ALIGN=MIDDLE  ALT=\"t=%28243-x%29%2F65\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But we already determined that these drive times are equal so we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F45=%28243-x%29%2F65 ALIGN=MIDDLE  ALT=\"x%2F45=%28243-x%29%2F65\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cross multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65x=45%28243-x%29 ALIGN=MIDDLE  ALT=\"65x=45%28243-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65x=10935-45x ALIGN=MIDDLE  ALT=\"65x=10935-45x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=110x=10935 ALIGN=MIDDLE  ALT=\"110x=10935\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From here on out, '=' means 'approximately equal to'\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=99.41 ALIGN=MIDDLE  ALT=\"x=99.41\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or Bob drove <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99.41 ALIGN=MIDDLE  ALT=\"99.41\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles to the meeting point.\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=d%2Fr ALIGN=MIDDLE  ALT=\"t=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Bob's travel time must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=99.41%2F45 ALIGN=MIDDLE  ALT=\"t=99.41%2F45\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2.21 ALIGN=MIDDLE  ALT=\"t=2.21\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.21 ALIGN=MIDDLE  ALT=\".21\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.21+%2A+60=12.6 ALIGN=MIDDLE  ALT=\".21+%2A+60=12.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes, and since they started at straight up noon, they must have met at 2:12.6 PM, and they met 99.41 miles from Bob's starting point.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Since they met at 99.41 miles from Bob's starting point, they must have met 243 - 99.41 = 143.59 miles from Joe's starting point.  If Joe travelled for 2.21 hours at 65 mph, he travelled <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.21+%2A+65+=+143.59 ALIGN=MIDDLE  ALT=\"2.21+%2A+65+=+143.59\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles.  Answer checks.  (Actually, if you just plug in the numbers given, the calculator shows a bit of error, but if you do the arithmetic from the beginning on the calculator and never round off until the end, it all comes out correctly) </SPAN>\n" );
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