document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239415>Question 239415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A biker completed a trip from town A to town B. If he rode 3 km per hour faster, then he could spend one hour less for this trip. If he rode 2 km per hour slower, he would be one hour late.<BR>\n" );
document.write( "Find the distance between towns, speed of the biker, and time of traveling.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175836 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=175836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A biker completed a trip from town A to town B.<BR>\n" );
document.write( " If he rode 3 km per hour faster, then he could spend one hour less for this trip. <BR>\n" );
document.write( "If he rode 2 km per hour slower, he would be one hour late.\r<BR>\n" );
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document.write( "Find the distance between towns, speed of the biker, and time of traveling.<BR>\n" );
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document.write( "Let s = the biker's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+3) = 3 km faster speed<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(s-2) = 2 km slower speed<BR>\n" );
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document.write( "Let d = dist from a to b<BR>\n" );
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document.write( "Write two time equations: time = dist/speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28s%2B3%29 ALIGN=MIDDLE  ALT=\"d%2F%28s%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 (he went 3 km/h faster)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28s-2%29 ALIGN=MIDDLE  ALT=\"d%2F%28s-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 (he went 2 km/hr slower)<BR>\n" );
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document.write( "Both equations = 1, so we can write it:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28s%2B3%29 ALIGN=MIDDLE  ALT=\"d%2F%28s%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28s-2%29 ALIGN=MIDDLE  ALT=\"d%2F%28s-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify, divide each term by d<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fs ALIGN=MIDDLE  ALT=\"1%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28s%2B3%29 ALIGN=MIDDLE  ALT=\"1%2F%28s%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28s-2%29 ALIGN=MIDDLE  ALT=\"1%2F%28s-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fs ALIGN=MIDDLE  ALT=\"1%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fs ALIGN=MIDDLE  ALT=\"1%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fs ALIGN=MIDDLE  ALT=\"1%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28s%2B3%29 ALIGN=MIDDLE  ALT=\"1%2F%28s%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28s-2%29 ALIGN=MIDDLE  ALT=\"1%2F%28s-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fs ALIGN=MIDDLE  ALT=\"2%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28s%2B3%29 ALIGN=MIDDLE  ALT=\"1%2F%28s%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28s-2%29 ALIGN=MIDDLE  ALT=\"1%2F%28s-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply by s(s+3)(s-2) to get rid of the denominators:<BR>\n" );
document.write( "2(s+3)(s-2) - s(s-2) = s(s+3)<BR>\n" );
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document.write( "2(s^2 + s - 6) - s^2 + 2s = s^2 + 3s<BR>\n" );
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document.write( "2s^2 + 2s - 12 - s^2 + 2s = s^2 + 3s<BR>\n" );
document.write( "Combine like terms on the left<BR>\n" );
document.write( "2s^2 - s^2 - s^2 + 2s + 2s - 3s - 12 = 0<BR>\n" );
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document.write( "s - 12 = 0<BR>\n" );
document.write( "s = 12 km/hr is the speed<BR>\n" );
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document.write( "Find the dist between towns using<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28s%2B3%29 ALIGN=MIDDLE  ALT=\"d%2F%28s%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ": <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F12 ALIGN=MIDDLE  ALT=\"d%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%2815%29 ALIGN=MIDDLE  ALT=\"d%2F%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by 60 <BR>\n" );
document.write( "5d - 4d = 60<BR>\n" );
document.write( "d = 60 km is the distance<BR>\n" );
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document.write( "Find the time: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F12 ALIGN=MIDDLE  ALT=\"60%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5 hrs, time of travel<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solutions in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28s-2%29 ALIGN=MIDDLE  ALT=\"d%2F%28s-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fs ALIGN=MIDDLE  ALT=\"d%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F10 ALIGN=MIDDLE  ALT=\"60%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F12 ALIGN=MIDDLE  ALT=\"60%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "6 - 5 = 1 hr <BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );