document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203094>Question 203094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me write out and solve the equation for this word problem?\r<BR>\n" );
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document.write( "A car leaves a town traveling at 60 miles per hour. How long will it take a second car traveling at 75 miles per hour to catch up to the first car if it leaves 2 hours later?\r<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 #153227 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=153227\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's make t = time (in hours) that the first car travels.\r<BR>\n" );
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document.write( "First, let's set up the equation for the first car to leave. Recall that the distance \"d\" equals the speed \"r\" multiplied by the time \"t\". So this means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   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=d=60t ALIGN=MIDDLE  ALT=\"d=60t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=60 ALIGN=MIDDLE  ALT=\"r=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the speed of the first car)\r<BR>\n" );
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document.write( "Now let's set up the second equation (for the second car). Since the first car travels \"t\" hours, and it has a 2 hour head start, this means that the second car is going to travel \"t-2\" hours (eg, the first car travels t=6 hours and the second travels t-2=6-2=4 hours). \r<BR>\n" );
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document.write( "So this means that we start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > and plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=75 ALIGN=MIDDLE  ALT=\"r=75\"   DISABLED_style= \"max-width:90%; height:auto;\" > and replace \"t\" with \"t-2\" to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=75%28t-2%29 ALIGN=MIDDLE  ALT=\"d=75%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: the \"d\"s of both equations are the same \"d\" since the cars will have gone the distance when they meet.\r<BR>\n" );
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document.write( "So we have the two equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=60t ALIGN=MIDDLE  ALT=\"d=60t\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=75%28t-2%29 ALIGN=MIDDLE  ALT=\"d=75%28t-2%29\"   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=d=60t ALIGN=MIDDLE  ALT=\"d=60t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%28t-2%29=60t ALIGN=MIDDLE  ALT=\"75%28t-2%29=60t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=75%28t-2%29 ALIGN=MIDDLE  ALT=\"d=75%28t-2%29\"   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=75t-150=60t ALIGN=MIDDLE  ALT=\"75t-150=60t\"   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=75t=60t%2B150 ALIGN=MIDDLE  ALT=\"75t=60t%2B150\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150 ALIGN=MIDDLE  ALT=\"150\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75t-60t=150 ALIGN=MIDDLE  ALT=\"75t-60t=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60t ALIGN=MIDDLE  ALT=\"60t\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15t=150 ALIGN=MIDDLE  ALT=\"15t=150\"   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=t=%28150%29%2F%2815%29 ALIGN=MIDDLE  ALT=\"t=%28150%29%2F%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   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=t=10 ALIGN=MIDDLE  ALT=\"t=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=10 ALIGN=MIDDLE  ALT=\"t=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the first car traveled for 10 hours\r<BR>\n" );
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document.write( "Subtract 2 from this answer to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-2=8 ALIGN=MIDDLE  ALT=\"10-2=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this tells us that the second car traveled 8 hours.\r<BR>\n" );
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document.write( "So it takes 8 hours for the second car to catch up and meet the first car. </SPAN>\n" );
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