document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=665081>Question 665081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two cars leave an intersection, one traveling west and the other south. After some time the faster car is 3 mi farther away from the intersection than the slower car. At the time the two cars where 15 miles apart.<BR>\n" );
document.write( " How far did each car travel?<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 #413760 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=413760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  two cars leave an intersection, one traveling west and the other south.<BR>\n" );
document.write( " After some time the faster car is 3 mi farther away from the intersection than the slower car.<BR>\n" );
document.write( " At the time the two cars where 15 miles apart. How far did each car travel?<BR>\n" );
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document.write( "Let d = distance traveled by the 1st car when they were 15 mi apart<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(d+3) = distance traveled by the faster car<BR>\n" );
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document.write( "This is pythag problem: a^2 + b^2 = c^2, where<BR>\n" );
document.write( "a = d<BR>\n" );
document.write( "b = (d+3)<BR>\n" );
document.write( "c = 15 <BR>\n" );
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document.write( "d^2 + (d+3)^2 = 15^2<BR>\n" );
document.write( "FOIL(d+3)(d+3)<BR>\n" );
document.write( "d^2 + d^2 + 3d + 3d + 9 = 225<BR>\n" );
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document.write( "2d^2 + 6d + 9 - 225 = 0<BR>\n" );
document.write( "2d^2 + 6d - 216 = 0<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "d^2 + 3d - 108 = 0<BR>\n" );
document.write( "this will factor to<BR>\n" );
document.write( "(d+12)(d-9) = 0<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "d = 9 mi, and 12 mi when they were 15 mi apart<BR>\n" );
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document.write( "Check this on a calc; enter<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%5E2%2B12%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%289%5E2%2B12%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > results: 15 </SPAN>\n" );
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