document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=215308>Question 215308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A family drove 1080 miles to their vacation lodge.  Bercause of increased traffic denisty, their average speed on the return trip was decreased by 6 miles per hour and the trip took 2 1/2 hours longer.  Determine their average speed on the way to the lodge. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162673 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=162673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Velocity  =  Distance / Time,,,,or  T=d/v<BR>\n" );
document.write( ".<BR>\n" );
document.write( "t1 = d/v1 = 1080/v1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "but  t2= t1+2.5,,,,,,v2=v1-6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "t2 = d/t2,,,,,(t1+2.5) = 1080/(v1-6),,,,,subst  <BR>\n" );
document.write( ".<BR>\n" );
document.write( "{(1080/v1) +2.5} = 1080/(v1-6)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "{ (1080+2.5v1)/v1} = 1080/(v1-6),,,,,mult  thru  by (v1-6) * (v1)<BR>\n" );
document.write( ".(1080+2.5v1)*(v1-6) = 1080 *(v1)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( ".<BR>\n" );
document.write( "1080v1 -6*1080 +2.5v1^2 -6*2.5v1 = 1080v1<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".6480 +2.5v1^2 -15v1 =0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2.5 v1^2 -15v1 +6480 =0,,,,,,divide  by  2.5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "v1^2 -6v1 +2592 =0,,,,factor<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(v1 - 54)(v1-48) = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "v1= 48,   54<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "check,,,(48),,,t1= 1080/48 = 22.5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "t2= 1080/ (48-6)=25.71,,,,3.2 difference,,,,not  valid<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(54) t1=1080/54 = 20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "t2 = 1080/(54-6) = 22.5,,,difference = 2.5,,,,ok<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Therefore  v1=54 MPH<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );