document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=963557>Question 963557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kelly rollerblades for 12 miles, then slows down by 4 miles per hour for another 6 miles. The slower portion takes 15 minutes less than the first part. Find the total time she spent rollerblading, if you know it was not more than 1 hour and 30 minutes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588749 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=588749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Kelly rollerblades for 12 miles, then slows down by 4 miles per hour for another 6 miles.<BR>\n" );
document.write( " The slower portion takes 15 minutes less than the first part.<BR>\n" );
document.write( " Find the total time she spent rollerblading, if you know it was not more than 1 hour and 30 minutes.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let s = speed on the first 12 mi<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-4) = speed on te last 6 mi<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Change 15 min to 1/4hr<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "fast speed time = slower speed time +  1/4 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fs ALIGN=MIDDLE  ALT=\"12%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28%28s-4%29%29 ALIGN=MIDDLE  ALT=\"6%2F%28%28s-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply equation by 4s(s-4), cancel the denominators and we have:<BR>\n" );
document.write( "12*4(s-4) = 6(4s) + s(s-4)<BR>\n" );
document.write( "12(4s-16) = 24s + s^2 - 4s<BR>\n" );
document.write( "48s - 192 =  s^2 + 20s<BR>\n" );
document.write( "Combine on the right to form a quadratic equation<BR>\n" );
document.write( "0 = s^2 + 20s - 48s + 192 <BR>\n" );
document.write( "s^2 - 28s + 192 = 0<BR>\n" );
document.write( "This will factor to<BR>\n" );
document.write( "(s-12)(s-16) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "s = 12 mph<BR>\n" );
document.write( "or <BR>\n" );
document.write( "s = 16 mph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Lets use the faster speed s=16 mph for the first 12 mi, and 12 mph for the last 6<BR>\n" );
document.write( "Find the times<BR>\n" );
document.write( "12/16 = .75 hrs<BR>\n" );
document.write( "6/12  = .50 hr<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "tot time: 1.25 hrs, 1 hr 15 min<BR>\n" );
document.write( "less than 1 hr 30 min </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );