document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211759>Question 211759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pat travels 70 miles on her milk route and Bob travels 75 miles on his route. Pat travels 5 miles per hour slower than Bob, and her route takes ½ hour longer than Bob’s. Find the speed at which each of them is traveling.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160077 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=160077\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Pat travels 70 miles on her milk route and Bob travels 75 miles on his route.<BR>\n" );
document.write( " Pat travels 5 miles per hour slower than Bob, and her route takes ½ hour longer than Bob’s.<BR>\n" );
document.write( " Find the speed at which each of them is traveling.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = Pat's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+5) = Bob's speed <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation; Time = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dist%2Fspeed ALIGN=MIDDLE  ALT=\"dist%2Fspeed\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Pat's time - Bob's time = one half hour<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2Fs%29 ALIGN=MIDDLE  ALT=\"70%2Fs%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"75%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .5<BR>\n" );
document.write( "Multiply equation by s(s+5), results:<BR>\n" );
document.write( "70(s+5) - 75s = .5s(s+5)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "70s + 350 - 75s = .5s^2 + 2.5s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "-5s + 350 = .5s^2 + 2.5s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "arrange as a quadratic equation<BR>\n" );
document.write( ".5s^2 + 2.5s + 5s - 350 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".5s^2 + 7.5s - 350 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply by 2, get rid of the decimals<BR>\n" );
document.write( "s^2 + 15s - 700 = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(s+35)(s-20) = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "positive solution<BR>\n" );
document.write( "s = 20 mph is Pat's speed<BR>\n" );
document.write( "and<BR>\n" );
document.write( "20 + 5 = 25 mph is Bob's speed<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solutions, find the times of each<BR>\n" );
document.write( "70/20 = 3.5 hr<BR>\n" );
document.write( "75/25 = 3.0<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "diff: = .5 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );