document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118052>Question 118052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cars started from the same point and traveled on a straight course in<BR>\n" );
document.write( "opposite directions for exactly 2 hours, at which time they were 208 miles<BR>\n" );
document.write( "apart. If one car traveled, on average, 8 miles per hour faster than the other<BR>\n" );
document.write( "car, what was the average speed for each car for the 2-hour trip?\r<BR>\n" );
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document.write( "I set up two equations A and B being rates in MPH<BR>\n" );
document.write( "equation 1-- multiplied times 2 to get it A and B in distances instead of rate.<BR>\n" );
document.write( "equation 2-- set this equation to get the relationship between rates\r<BR>\n" );
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document.write( "Equation 1: 2A+2B=208               <BR>\n" );
document.write( "Equation 2: A=8+B                   \r<BR>\n" );
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document.write( "then solved by plugging Equation 2 into Equation 1\r<BR>\n" );
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document.write( "got B = 23 and A = 31<BR>\n" );
document.write( "which according to my answer key is not right, it says 48 and 56. I am missing some stupid detail somewhere can you help me out. It doesn't matter which is A or B. Thanks a lot for your help<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 #86127 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=speed of first car, y=speed of second car\r<BR>\n" );
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document.write( "You're on the right track since you have the correct equations set up\r<BR>\n" );
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document.write( "Start with the given system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y=208 ALIGN=MIDDLE  ALT=\"2x%2B2y=208\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2By ALIGN=MIDDLE  ALT=\"x=8%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%288%2By%29%2B2y=208 ALIGN=MIDDLE  ALT=\"2%288%2By%29%2B2y=208\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2By ALIGN=MIDDLE  ALT=\"x=8%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2By ALIGN=MIDDLE  ALT=\"8%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2B2y%2B2y=208 ALIGN=MIDDLE  ALT=\"16%2B2y%2B2y=208\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B16=208 ALIGN=MIDDLE  ALT=\"4y%2B16=208\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=208-16 ALIGN=MIDDLE  ALT=\"4y=208-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 16 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=192 ALIGN=MIDDLE  ALT=\"4y=192\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28192%29%2F%284%29 ALIGN=MIDDLE  ALT=\"y=%28192%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 to isolate y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=48 ALIGN=MIDDLE  ALT=\"y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Now that we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=48 ALIGN=MIDDLE  ALT=\"y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can plug this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2By ALIGN=MIDDLE  ALT=\"x=8%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2B%2848%29 ALIGN=MIDDLE  ALT=\"x=8%2B%2848%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   DISABLED_style= \"max-width:90%; height:auto;\" > for each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=56 ALIGN=MIDDLE  ALT=\"x=56\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=56 ALIGN=MIDDLE  ALT=\"x=56\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=48 ALIGN=MIDDLE  ALT=\"y=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the first car was going 56 mph and the second car was going 48 mph </SPAN>\n" );
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