document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30904>Question 30904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cars start together and travel in the same direction, one going twice as fast as the other.  At the end of 3 hours, they are 96 miles apart.  How fast is each car traveling? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17658 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><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=17658\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "The previous solution you got for this question (\"The fast car is travelling at 21 and 1/3 miles an hour\", etc) is actually incorrect.\r<BR>\n" );
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document.write( "Let's call X to the the speed of the faster car, and Y to the speed of the other one, both measured in miles per hour. After 3 hours, the fast car has traveled a distance of 3X miles, and the slow car has traveled a distance of 3Y miles.\r<BR>\n" );
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document.write( "Now, since they are 96 miles apart, the equation that describes this is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3X+-+3Y+=+96+ ALIGN=MIDDLE  ALT=\"3X+-+3Y+=+96+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The other equation (\"one going twice as fast as the other\") is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+=+2Y ALIGN=MIDDLE  ALT=\"X+=+2Y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[recall that X is the fast car]\r<BR>\n" );
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document.write( "So we have the system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%283X+-+3Y+=+96+%2CX+=+2Y%29 ALIGN=MIDDLE  ALT=\"system%283X+-+3Y+=+96+%2CX+=+2Y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting the 2nd equation into the 1st one, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%282Y%29+-+3Y+=+96 ALIGN=MIDDLE  ALT=\"3%282Y%29+-+3Y+=+96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6Y+-+3Y+=+96 ALIGN=MIDDLE  ALT=\"6Y+-+3Y+=+96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3Y+=+96 ALIGN=MIDDLE  ALT=\"3Y+=+96\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+32 ALIGN=MIDDLE  ALT=\"Y+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the slow car is traveling at 32 mph, and the fast car is traveling at 64 mph.\r<BR>\n" );
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document.write( "I hope this helps!\r<BR>\n" );
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document.write( "Get more answers at <a  rel=nofollow HREF=http://www.onlinemathanswers.com>Online Math Answers.com</a>!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );