document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=737280>Question 737280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A truck left city a and b respectively, at the same time traveling toward each other. When they met, the track had traveled 120 more miles than the van. Afterwards, the van traveled 9 more hours to reach city B while the truck traveled 4 more hours to reach city A. What is the distance between the 2 cities?\r<BR>\n" );
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document.write( "PLEASE HELP!!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #450295 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=450295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A van and a truck left city a and b respectively at the same time traveling toward each other.<BR>\n" );
document.write( " When they met, the truck had traveled 120 more miles than the van.<BR>\n" );
document.write( " Afterwards, the van traveled 9 more hours to reach city B while the truck traveled 4 more hours to reach city A. <BR>\n" );
document.write( " What is the distance between the 2 cities?<BR>\n" );
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document.write( "let x = distance from a to meeting point (initially traveled by the van)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+120) = distance from b to meeting point (initially traveled by the truck)<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "(2x+120) = distance from a to b<BR>\n" );
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document.write( "Speed = dist/time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B120%29%2F9 ALIGN=MIDDLE  ALT=\"%28x%2B120%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > = speed of the van traveling to b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F4 ALIGN=MIDDLE  ALT=\"x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = speed of the truck traveling to a<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let t = travel time for both to the meeting point (time = dist/speed)<BR>\n" );
document.write( "Truck time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B120%29%2F%28x%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%2B120%29%2F%28x%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (x+120)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fx ALIGN=MIDDLE  ALT=\"4%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2B480%29%2Fx ALIGN=MIDDLE  ALT=\"%284x%2B480%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Van time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%28x%2B120%29%2F9%29 ALIGN=MIDDLE  ALT=\"x%2F%28%28x%2B120%29%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%28x%2B120%29 ALIGN=MIDDLE  ALT=\"9%2F%28x%2B120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%29%2F%28x%2B120%29 ALIGN=MIDDLE  ALT=\"%289x%29%2F%28x%2B120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Times are equal, therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%2B480%29%2Fx ALIGN=MIDDLE  ALT=\"%284x%2B480%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%29%2F%28x%2B120%29 ALIGN=MIDDLE  ALT=\"%289x%29%2F%28x%2B120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "9x^2 = (4x+480)(x+120)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "9x^2 = 4x^2 + 480x + 480x + 57600<BR>\n" );
document.write( "0 = 4x^2 - 9x^2 + 960x + 57600<BR>\n" );
document.write( "-5x^2 + 960x + 57600 = 0<BR>\n" );
document.write( "simplify, divide by-5<BR>\n" );
document.write( "x^2 - 192x - 11520 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x-240)(x+48) = 0<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "x = 240<BR>\n" );
document.write( "a to b distance; 2(240) + 120 = 600 miles<BR>\n" );
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document.write( "We can confirm this, find the speed of each<BR>\n" );
document.write( "240/4 = 60 km/hr the truck<BR>\n" );
document.write( "360/9 = 40 km/hr the van<BR>\n" );
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document.write( "Time to meet point should be the same<BR>\n" );
document.write( "truck: 360/60 = 6 hrs<BR>\n" );
document.write( "van: 240/40 = 6 hrs<BR>\n" );
document.write( "  </SPAN>\n" );
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