document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=433362>Question 433362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2 cars start at the same time from towns a and b, and travel with constant but different speeds towards each other. They pass each other 70 km from town a, and continue to the opposite town, where they turn around without stopping. The cars pass each other again 40 km from town b. What is the distance between the 2 towns? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300464 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=300464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Cars start at the same time from towns a and b, and travel with constant but<BR>\n" );
document.write( " different speeds towards each other.<BR>\n" );
document.write( " They pass each other 70 km from town a, and continue to the opposite town,<BR>\n" );
document.write( " where they turn around without stopping.<BR>\n" );
document.write( " The cars pass each other again 40 km from town b.<BR>\n" );
document.write( " What is the distance between the 2 towns?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let d = distance from a to b<BR>\n" );
document.write( ":<BR>\n" );
document.write( "First time they meet:<BR>\n" );
document.write( "car 1 travels 70 km<BR>\n" );
document.write( "car 2 travels (d-70)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Second time they meet<BR>\n" );
document.write( "car 1 travels (d-70) + 40 = (d-30)<BR>\n" );
document.write( "car 2 travels 70 + (d-40) = (d+30)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The ratio of the distances traveled by the two cars remain the same; therefore:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28%28d-70%29%29 ALIGN=MIDDLE  ALT=\"70%2F%28%28d-70%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d-30%29%2F%28d%2B30%29 ALIGN=MIDDLE  ALT=\"%28d-30%29%2F%28d%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "70(d+30) = (d-70)(d-30)<BR>\n" );
document.write( "70d + 2100 = d^2 - 30d - 70d + 2100<BR>\n" );
document.write( "Subtract 2100 from both sides, arrange as a quadratic equation<BR>\n" );
document.write( "d^2 - 100d - 70d = 0<BR>\n" );
document.write( "d^2 - 170d = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "d(d - 170) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "d = 0, obviously not the solution<BR>\n" );
document.write( "and<BR>\n" );
document.write( "d = 170 km distance between the towns </SPAN>\n" );
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