document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724611>Question 724611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A trucker calculates that if he increased his average speed by 90 km/h,<BR>\n" );
document.write( "	he could travel his 660-km route in 7 h less time than his usual.<BR>\n" );
document.write( "	Find his usual speed (km/h). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443809 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=443809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r = the unknown usual speed.\r<BR>\n" );
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document.write( "______________rate______________time___________________distance<BR>\n" );
document.write( "Usual_________r_________________t______________________660<BR>\n" );
document.write( "Faster_______r+90______________t-7____________________660\r<BR>\n" );
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document.write( "We want to solve for r, but t is also a variable and unknown.  Fortunately, the rows of data use the SAME distance.  We can solve for the times in terms of distance and rates.  rate*time=distance.\r<BR>\n" );
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document.write( "t=660/r, so t-7=660/r-7.\r<BR>\n" );
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document.write( "______________rate______________time___________________distance<BR>\n" );
document.write( "Usual_________r_________________660/r______________________660<BR>\n" );
document.write( "Faster_______r+90______________660/r-7____________________660\r<BR>\n" );
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document.write( "The \"Faster\" data may be of use.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B90%29%2A%28660%2Fr-7%29=660 ALIGN=MIDDLE  ALT=\"%28r%2B90%29%2A%28660%2Fr-7%29=660\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "... WAIT!<BR>\n" );
document.write( "... Interrupting that, there are TWO equations possible:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rt=660 ALIGN=MIDDLE  ALT=\"rt=660\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B90%29%28t-7%29=660 ALIGN=MIDDLE  ALT=\"%28r%2B90%29%28t-7%29=660\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Going ahead with that system, the second equation becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rt-7r%2B90t-630=660 ALIGN=MIDDLE  ALT=\"rt-7r%2B90t-630=660\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rt%2B90t-7r=30 ALIGN=MIDDLE  ALT=\"rt%2B90t-7r=30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and from the first equation, find that t=660/r and substitute to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28660%2Fr%29%2B90%28660%2Fr%29-7r=30 ALIGN=MIDDLE  ALT=\"r%28660%2Fr%29%2B90%28660%2Fr%29-7r=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=660%2B90%2A660%2Fr-7r=30 ALIGN=MIDDLE  ALT=\"660%2B90%2A660%2Fr-7r=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=660r%2B90%2A660-7r%5E2=30 ALIGN=MIDDLE  ALT=\"660r%2B90%2A660-7r%5E2=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7r%5E2%2B660r%2B90%2A660-30=0 ALIGN=MIDDLE  ALT=\"-7r%5E2%2B660r%2B90%2A660-30=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7r%5E2%2B660r%2B59370=0 ALIGN=MIDDLE  ALT=\"-7r%5E2%2B660r%2B59370=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%287r%5E2-660r-59370=0%29 ALIGN=MIDDLE  ALT=\"highlight%287r%5E2-660r-59370=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using general solution to quadratic equation, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=150%29 ALIGN=MIDDLE  ALT=\"highlight%28r=150%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/hr\r<BR>\n" );
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document.write( "I have not yet tried to check that solution.<BR>\n" );
document.write( " </SPAN>\n" );
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