document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=670747>Question 670747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 19. Two hikers leave town A at the same time and walk by two different routes to town B. The average speed of one hiker is 1 mile per hour more than the average speed of the other hiker. The slower hiker reaches town B 1/2 hour before the faster hiker, because the route taken by the faster hiker is 15 miles long, while the route taken by the slower hiker is only 10 miles long. What is the average speed of each hiker?<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 #417204 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=417204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 19. Two hikers leave town A at the same time and walk by two different routes to town B.<BR>\n" );
document.write( " The average speed of one hiker is 1 mile per hour more than the average speed<BR>\n" );
document.write( " of the other hiker. The slower hiker reaches town B 1/2 hour before the faster hiker, because the route taken by the faster hiker is 15 miles long, while the route taken by the slower hiker is only 10 miles long.<BR>\n" );
document.write( " What is the average speed of each hiker?<BR>\n" );
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document.write( "Let s = be that average speed of the slow hiker<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+1) = average speed of the other hiker<BR>\n" );
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document.write( "Write time equation; time = dist/speed<BR>\n" );
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document.write( "Fast hiker time = slow hiker time +.5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F%28%28s%2B1%29%29 ALIGN=MIDDLE  ALT=\"15%2F%28%28s%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fs ALIGN=MIDDLE  ALT=\"10%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5<BR>\n" );
document.write( "multiply by s(s+1) to clear the denominators<BR>\n" );
document.write( "15s = 10(s+1) + .5s(s+1)<BR>\n" );
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document.write( "15s = 10s + 10 + .5s^2 + .5s<BR>\n" );
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document.write( "0 = 10s - 15s + 10 + .5s^2 + .5s<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( ".5s^2 + .5s - 5s + 10 = 0<BR>\n" );
document.write( ".5s^2 - 4.5s + 10 = 0<BR>\n" );
document.write( "Get rid of the decimals mult by 2<BR>\n" );
document.write( "s^2 - 9s + 20 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(s-4)(s-5) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "s = 4 mph, then the faster hiker is 5 mph<BR>\n" );
document.write( "and<BR>\n" );
document.write( "s = 5 mph, then the faster hiker is 6 mph<BR>\n" );
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document.write( "see both of those solutions work; find the time of each:<BR>\n" );
document.write( "10/4 = 2.5<BR>\n" );
document.write( "15/5 = 3.0<BR>\n" );
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document.write( "dif: .5 hrs<BR>\n" );
document.write( "and<BR>\n" );
document.write( "10/5 = 2.0 hrs<BR>\n" );
document.write( "15/6 = 2.5 hrs<BR>\n" );
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document.write( "dif: .5 hrs, so either solution is can be used </SPAN>\n" );
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