document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=65498>Question 65498</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534944949/algebrahomeworkh>Essential Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Abigail Nightwind has planned a bike trip with some friends from her village. They will bike for 8 hours, then hike for 4 hours. If they can bike on the average 10mph fater than they can hike and if they will cover a total of 122 miles, how fast can Abigail and her friends bike? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46041 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=46041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Abigail Nightwind has planned a bike trip with some friends from her village. They will bike for 8 hours, then hike for 4 hours. If they can bike on the average 10mph faster than they can hike and if they will cover a total of 122 miles, how fast can Abigail and her friends bike?<BR>\n" );
document.write( "The formula for distance is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=rt%29 ALIGN=MIDDLE  ALT=\"highlight%28d=rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where d=distance, r=rate(or speed), and t=time<BR>\n" );
document.write( "Givens for the hike protion:<BR>\n" );
document.write( "t=4<BR>\n" );
document.write( "r=r (we don't know it)<BR>\n" );
document.write( "d=4r<BR>\n" );
document.write( "Givens for the bike protion:<BR>\n" );
document.write( "t=8<BR>\n" );
document.write( "r=r+10 (10 mph faster than they can hike.)<BR>\n" );
document.write( "d=8(r+10)<BR>\n" );
document.write( "The total of the trip= 122<BR>\n" );
document.write( "Problem to solve:<BR>\n" );
document.write( "4r+8(r+10)=122<BR>\n" );
document.write( "4r+8r+80=122<BR>\n" );
document.write( "12r+80=122<BR>\n" );
document.write( "12r+80-80=122-80<BR>\n" );
document.write( "12r=42<BR>\n" );
document.write( "12r/12=42/12<BR>\n" );
document.write( "r=3.5<BR>\n" );
document.write( "Therefore the rate that they can bike: r+10=3.5+10=13.5 mph<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Sanity check:<BR>\n" );
document.write( "If they hiked for 4 hrs at 3.5 mph and biked for 8 hrs at 13.5 mph, would they travel 122 mi?<BR>\n" );
document.write( "4(3.5)+8(13.5)=122 ?<BR>\n" );
document.write( "14+108=122<BR>\n" );
document.write( "122=122  It appears we are sane.<BR>\n" );
document.write( "Happy Calculating!!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );