document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118332>Question 1118332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> they traveled the first 70 miles at a constant rate of speed for the remainder of the trip they ran into bad weather, and had to reduce speed by 30 mph for the last 12 miles of the trip. The trip took 2 hours. Find the rate of speed for each part of the trip. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733617 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=733617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> They traveled the first 70 miles at a constant rate of speed<BR>\n" );
document.write( " for the remainder of the trip they ran into bad weather, and had to reduce speed by 30 mph for the last 12 miles of the trip.<BR>\n" );
document.write( " The trip took 2 hours.<BR>\n" );
document.write( " Find the rate of speed for each part of the trip.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = the original speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-30) = the slower speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation: time = dist/speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2Fs ALIGN=MIDDLE  ALT=\"70%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s-30%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s-30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "multiply equation by s(s-30)<BR>\n" );
document.write( "s(s-30)* <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2Fs ALIGN=MIDDLE  ALT=\"70%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + s(s-30)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s-30%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s-30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2s(s-30)<BR>\n" );
document.write( "Cancel the denominators<BR>\n" );
document.write( "70(s-30) + 12s = 2s^2 - 60s<BR>\n" );
document.write( "70s - 2100 + 12s = 2s^2 - 60s<BR>\n" );
document.write( "82s - 2100 = 2s^2 - 60s<BR>\n" );
document.write( "0 = 2s^2 - 60s - 82s + 2100<BR>\n" );
document.write( " 2s^2 - 142s + 2100 = 0<BR>\n" );
document.write( "simplify, divide 2<BR>\n" );
document.write( "s^2 - 71s + 1050 = 0<BR>\n" );
document.write( "You can use the quadratic formula, but this will factor to<BR>\n" );
document.write( "(s-50)(s+21) = 0<BR>\n" );
document.write( "s = 50 mph for the first 70 mi<BR>\n" );
document.write( "then<BR>\n" );
document.write( "50 - 30 = 20 mph for the last 12 hrs<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check, find the actual time at each speed<BR>\n" );
document.write( "70/50 = 1.4 hrs<BR>\n" );
document.write( "12/20 = .6 hrs<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "trip time: 2 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );