document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=893809>Question 893809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A vehicle starts traveling from city A towards city B. It maintains a speed of 45 miles per hour. Another vehicle starts the same trip 45 minutes later going 70 miles per hour. Where (a distance from city A) will the faster vehicle take over the slower one. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541509 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=541509\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Many examples like this are requested.\r<BR>\n" );
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document.write( "The described problem can be generalized like this:<BR>\n" );
document.write( "A vehicle starts traveling from city A towards city B. It maintains a speed of r miles per hour.<BR>\n" );
document.write( " Another vehicle starts the same trip k <b>hours</b> later going R miles per hour.<BR>\n" );
document.write( "Where (a distance from city A) will the faster vehicle take over the slower one.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cr%3CR ALIGN=MIDDLE  ALT=\"0%3Cr%3CR\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E0 ALIGN=MIDDLE  ALT=\"k%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let d be the distance where the late fast car reaches the early slow car.<BR>\n" );
document.write( "t is unknown,<BR>\n" );
document.write( "d is unknown.\r<BR>\n" );
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document.write( "_________________speed________time_______distance<BR>\n" );
document.write( "EARLY SLOW________r___________t+k_________d<BR>\n" );
document.write( "LATE FAST_________R____________t__________d\r<BR>\n" );
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document.write( "EQUATIONS<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28t%2Bk%29=d ALIGN=MIDDLE  ALT=\"r%28t%2Bk%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Rt=d ALIGN=MIDDLE  ALT=\"Rt=d\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Solve for t and d.\r<BR>\n" );
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document.write( "Simply equating the two formulas for d,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28t%2Bk%29=Rt ALIGN=MIDDLE  ALT=\"r%28t%2Bk%29=Rt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rt%2Brk=Rt ALIGN=MIDDLE  ALT=\"rt%2Brk=Rt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rt%2Brk-Rt=0 ALIGN=MIDDLE  ALT=\"rt%2Brk-Rt=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rt-Rt=-rk ALIGN=MIDDLE  ALT=\"rt-Rt=-rk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%28r-R%29=-rk ALIGN=MIDDLE  ALT=\"t%28r-R%29=-rk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-rk%2F%28r-R%29 ALIGN=MIDDLE  ALT=\"t=-rk%2F%28r-R%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=rk%2F%28R-r%29%29 ALIGN=MIDDLE  ALT=\"highlight%28t=rk%2F%28R-r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use this result for t in either of the original equations to find d.<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=R%28rk%2F%28R-r%29%29 ALIGN=MIDDLE  ALT=\"d=R%28rk%2F%28R-r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=%28rRk%29%2F%28R-r%29%29 ALIGN=MIDDLE  ALT=\"highlight%28d=%28rRk%29%2F%28R-r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, d, the distance completely in symbolic form.\r<BR>\n" );
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document.write( "Now you can simply substitute the values from the problem description for r, R, and k, and evaluate d.<BR>\n" );
document.write( " </SPAN>\n" );
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