document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217867>Question 217867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three- hour head start.  How far from the starting point are the two vechicles. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164206 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10551)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=164206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three- hour head start.  How far from the starting point are the two vechicles. \r<BR>\n" );
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document.write( "Let the time that the faster vehicle (motorcycle) takes to get to the meeting point be T\r<BR>\n" );
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document.write( "Then the time that the car takes to get to the meeting point is T + 3 since it had a 3-hour head start, and is the slower vehicle\r<BR>\n" );
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document.write( "Since Distance = Speed x Time, and in this case the distances are equal, we therefore have: 70T = 40(T + 3)\r<BR>\n" );
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document.write( "70T = 40T + 120\r<BR>\n" );
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document.write( "30T  =  120\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+4 ALIGN=MIDDLE  ALT=\"T+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which makes the distance that both vehicles traveled, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28280%29 ALIGN=MIDDLE  ALT=\"highlight_green%28280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles, calculated as (70 * 4), or (40 * 7).\r<BR>\n" );
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document.write( "It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance. </SPAN>\n" );
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