document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139112>Question 139112</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 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 #101534 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=101534\">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 at a rate 10 mph slower. If loren had driven the entire trip they would have arrived 30 minutes sooner What was Loren's rate.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = Lor rate of speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-10) = Loi's rate of speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation: Time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Lor time + .5 hr = Lor's + Loi's time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fs ALIGN=MIDDLE  ALT=\"300%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fs ALIGN=MIDDLE  ALT=\"200%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F%28%28s-10%29%29 ALIGN=MIDDLE  ALT=\"100%2F%28%28s-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply equation by s(s-10) to get rid of the denominators<BR>\n" );
document.write( "s(s-10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fs ALIGN=MIDDLE  ALT=\"300%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5s(s-10) = s(s-10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fs ALIGN=MIDDLE  ALT=\"200%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + s(s-10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2F%28%28s-10%29%29 ALIGN=MIDDLE  ALT=\"100%2F%28%28s-10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel out the denominators and you have:<BR>\n" );
document.write( "300(s-10) + .5s^2 - 5s = 200(s-10) + 100s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "300s - 3000 + .5s^2 - 5s = 200s - 2000 + 100s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "group like terms on the left:<BR>\n" );
document.write( ".5s^2 + 300s - 5s - 200s - 100s - 3000 + 2000 = 0<BR>\n" );
document.write( ": <BR>\n" );
document.write( ".5s^2 - 5s - 1000 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply eq by 2, to make the coefficient of s^2 = 1<BR>\n" );
document.write( "s^2 - 10s - 2000 = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(s-50)(s+40) = 0<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "s = +50 mph is Lore's speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution by finding the times:<BR>\n" );
document.write( "200/50 + 100/40 = 6.5 hrs<BR>\n" );
document.write( "300/50 = 6 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );