document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171283>Question 171283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During the day, a truck driver encounters light, moderate, and heavy traffic. If he travels 1/3 hour in light traffic, 1/2 hour in moderate traffic, and 1/5 hour in heavy traffic, he can cover 21 miles. If he travels 1/5 hour in light, 1/4 hour in moderate, and 1 hour in heavy traffic, he can cover 16 miles. The sum of his speeds in moderate and heavy traffic is 5 miles per hour less than his speed in light traffic. Find his speed in each type of traffic. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126688 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=126688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d=rt.....this is our basic equation. In this instance we have to keep in mind that rates and times are different under different conditions<BR>\n" );
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document.write( "we are looking for the rates under different conditions. lets call the rates under light, moderate, and heavy conditions:L,M,and H respectively.  We are given 2 different distances along with there times. We will take this information and write two equations.  We are also give the fact that the sum of the speeds M+H equals 5 less than the speed in Light traffic L-5.<BR>\n" );
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document.write( "M+H=L-5--->L=M+H+5.........eq 1<BR>\n" );
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document.write( "(1/3)L+(1/2)M+(1/5)H=21....eq 2---->this is the rates and times of each added<BR>\n" );
document.write( "....................................together to equal the distance...rt=d<BR>\n" );
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document.write( "(1/5)L+(1/4)M+(1)H=16......eq 3<BR>\n" );
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document.write( "Lets get rid of the fractional parts in eq 2 and 3 by multiplying eq 2 by 30 and eq 3 by 20....Least common multiples.<BR>\n" );
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document.write( "10L+15M+6H=630....revised eq 2<BR>\n" );
document.write( "4L+5M+20H=320.....revised eq 3 <BR>\n" );
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document.write( "Now lets take L's value from eq 1 and plug it into revised eq 2 and eq 3.<BR>\n" );
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document.write( "10(M+H+5)+15M+6H=630-->distribute-->10M+10H+50+15M+6H=630<BR>\n" );
document.write( "4(M+H+5)+5M+20H=320--->distribute--->4M+4H+20+5M+20M=320<BR>\n" );
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document.write( "after combining the terms we arrive at:<BR>\n" );
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document.write( "25M+16H=580.(4).mult this eq by 3..we are doing this to eliminate the H terms <BR>\n" );
document.write( "9M+24H=300..(5)..multiply this eq by -2<BR>\n" );
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document.write( "What folllows is what we have left as the H terms cancel out 48H-48H=0<BR>\n" );
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document.write( "3(25M)+(-2)9M=3(580)+(-2)300<BR>\n" );
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document.write( "75M-18M=1140<BR>\n" );
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document.write( "57M=1140<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28M=20%29 ALIGN=MIDDLE  ALT=\"highlight%28M=20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "now we plug M's found value into either equation marked (4) or (5)...I chose (5)<BR>\n" );
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document.write( "9(20)+24H=300---->24H=300-180--->24H=120<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28H=5%29 ALIGN=MIDDLE  ALT=\"highlight%28H=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now plug M's and H's found values into eq 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L=20%2B5%2B5=30%29 ALIGN=MIDDLE  ALT=\"highlight%28L=20%2B5%2B5=30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "speeds for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" >ight, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >oderate and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H ALIGN=MIDDLE  ALT=\"H\"   DISABLED_style= \"max-width:90%; height:auto;\" >eavy traffic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28L=30%2CM=20%2CH=5%29 ALIGN=MIDDLE  ALT=\"system%28L=30%2CM=20%2CH=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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