document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203097>Question 203097</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 mph slower.  If Loren had driven for the entire trip, they would have arrived 30 minutes sooner.  What was Loren's rate? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153278 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=153278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles<BR>\n" );
document.write( " at a rate 10 mph slower. If Loren had driven for the entire trip,<BR>\n" );
document.write( " they would have arrived 30 minutes sooner. What was Loren's rate?<BR>\n" );
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document.write( "Let r = Loren's rate<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(r-10) = Lois' rate<BR>\n" );
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document.write( "Write a time equation: Time = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dist%2Frate ALIGN=MIDDLE  ALT=\"dist%2Frate\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Convert 30 min to .5 hrs<BR>\n" );
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document.write( "Loren's drive time + Lois drive time = Loren's drive time + 30 min (.5 hr)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fr ALIGN=MIDDLE  ALT=\"200%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F%28%28r-10%29%29 ALIGN=MIDDLE  ALT=\"100%2F%28%28r-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fr ALIGN=MIDDLE  ALT=\"300%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5<BR>\n" );
document.write( "multiply equation by: r(r-10), results<BR>\n" );
document.write( "200(r-10) + 100r = 300(r-10) + .5r(r-10)<BR>\n" );
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document.write( "200r - 2000 + 100r = 300r - 3000 + .5r^2 - 5r<BR>\n" );
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document.write( "300r - 2000 = 300r - 3000 + .5r^2 - 5r<BR>\n" );
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document.write( "0 = 300r - 300r - 3000 + 2000 .5r^2 - 5r <BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( ".5r^2 - 5r - 1000 = 0<BR>\n" );
document.write( "Multiply by 2 to get rid of the decimal<BR>\n" );
document.write( "r^2 - 10r - 2000 = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(r-50)(r+40) = 0<BR>\n" );
document.write( "Positive solution<BR>\n" );
document.write( "r = 50 mph is Loren's speed<BR>\n" );
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document.write( "Check solution in original equation (40 mph is Lois' speed)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F50 ALIGN=MIDDLE  ALT=\"200%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F40 ALIGN=MIDDLE  ALT=\"100%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F50 ALIGN=MIDDLE  ALT=\"300%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5<BR>\n" );
document.write( "4 + 2.5 = 6 + .5<BR>\n" );
document.write( " </SPAN>\n" );
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