document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=682048>Question 682048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At the same time, but different speed, Mark and Nancy left (driving) from different towns, A and B, and drove toward each other.  They first met at the point that was 60 miles from Town A.  When Mark and Nancy reached their destinations (B and A, respectively) they drove back without stop.  3 hours later after  they originally left the towns (the initial staring points), they met again.  This time, the meeting point was 40 miles from town A.  Suppose each of them was moving all the time at a constant speed, what were the speeds of Mark and Nancy. (note, they have different speeds).<BR>\n" );
document.write( "Thanks for your help!  It is much appreciated!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #423014 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=423014\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At the same time, but different speed, Mark and Nancy left (driving) from different towns, A and B, and drove toward each other.<BR>\n" );
document.write( " They first met at the point that was 60 miles from Town A.<BR>\n" );
document.write( " When Mark and Nancy reached their destinations (B and A, respectively) they drove back without stop.<BR>\n" );
document.write( " 3 hours later after they originally left the towns (the initial staring points), they met again.<BR>\n" );
document.write( " This time, the meeting point was 40 miles from town A. Suppose each of them was moving all the time at a constant speed, what were the speeds of Mark and Nancy.\r<BR>\n" );
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document.write( "A diagram will help<BR>\n" );
document.write( "A------60------*-----d------B; first meeting<BR>\n" );
document.write( "A----40----*----(d+20)------B: 2nd meeting<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let d = distance from the 1st meeting point to B, therefore<BR>\n" );
document.write( "Initially, M travels 60 mi while N travels d mi<BR>\n" );
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document.write( "To the 2nd meeting:<BR>\n" );
document.write( "M travels: d + (d+20) = (2d+20) mi<BR>\n" );
document.write( "while<BR>\n" );
document.write( "N travels: 60 + 40 = 100 mi\r<BR>\n" );
document.write( "\n" );
document.write( ":<BR>\n" );
document.write( "The M:N distance relationships are the same for each part of the trip<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1st meeting = 2nd meeting<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2Fd ALIGN=MIDDLE  ALT=\"60%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282d%2B20%29%2F100 ALIGN=MIDDLE  ALT=\"%282d%2B20%29%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "d(2d+20) = 60 * 100<BR>\n" );
document.write( "2d^2 + 20d = 6000<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "2d^2 + 20d - 6000 = 0<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "d^2 + 10d - 3000 = 0<BR>\n" );
document.write( "This will factor to<BR>\n" );
document.write( "(d+60)(d-50) = 0<BR>\n" );
document.write( "the positive solution<BR>\n" );
document.write( "d = 50 miles from the 1st meeting point to B<BR>\n" );
document.write( "then<BR>\n" );
document.write( "60 + 2(50) + 20 = 180 miles traveled by M in 3 hrs, therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F3 ALIGN=MIDDLE  ALT=\"180%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 60 mph is M's speed<BR>\n" );
document.write( "And<BR>\n" );
document.write( "50 + 60 + 40 = 150 miles traveled by N in 3 hrs, therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F3 ALIGN=MIDDLE  ALT=\"150%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 50 mph is N's speed<BR>\n" );
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