document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=744896>Question 744896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cars leave an intersection. one travels north; the other car travels west. when the car traveling north had gone 48 miles, the distance between the cars was 8 miles more than three times the distance traveled by the car heading west. find the distance between the cars at that time.<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 #453721 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=453721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two cars leave an intersection. one travels north; the other car travels west.<BR>\n" );
document.write( " when the car traveling north had gone 48 miles, the distance between the cars was 8 miles more than three times the distance traveled by the car heading west.<BR>\n" );
document.write( " find the distance between the cars at that time.<BR>\n" );
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document.write( "This is a pythag problem, the distance between the cars is the hypotenuse<BR>\n" );
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document.write( "let w = the distance traveled by the westbound car<BR>\n" );
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document.write( "\"the distance between the cars was 8 miles more than three times the distance traveled by the car heading west.\" therefore<BR>\n" );
document.write( "3w + 8 = the distance between the cars<BR>\n" );
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document.write( "48^2 + w^2 = (3w+8)^2<BR>\n" );
document.write( "FOIL (3w+8)(3w+8)<BR>\n" );
document.write( "2304 + w^2 = 9w^2 + 48w + 64<BR>\n" );
document.write( "2304 = 9w^2 - w^2 + 24w + 64<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "8w^2 + 48w + 64 - 2304 = 0<BR>\n" );
document.write( "8w^2 + 48w - 2240 = 0<BR>\n" );
document.write( "Simplify, divide by 8:<BR>\n" );
document.write( "w^2 + 6w - 280 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(w+20)(w-14) = 0<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "w = 14 mi traveled by the west bound car<BR>\n" );
document.write( "then<BR>\n" );
document.write( "3(14) + 8 = 50 mi between the cars<BR>\n" );
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document.write( "See if that checks out on a calc<BR>\n" );
document.write( "enter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2848%5E2%2B14%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2848%5E2%2B14%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > results is 50, confirms our solution<BR>\n" );
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