document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=516178>Question 516178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two riders depart from city a to city b. One rider rides at 12 mph and other rider at 18 mph. Slower rider takes 1.5 hours longer to ride the distance.<BR>\n" );
document.write( "How long did it take both riders to reach the destination<BR>\n" );
document.write( "How far is city a to city b?\r<BR>\n" );
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document.write( "HELP!!!! How am I supposed to figure out how far the cities are from each other without any information on one or the other? And 1.5 hours to ride the distance??? AARRRGGGHHHH!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344279 by </B><A HREF=/tutors/aboutme.mpl?userid=gc2000><B>gc2000(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gc2000><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=gc2000><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=344279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = time for rider 1 to city b<BR>\n" );
document.write( "y = time for rider 2 to city b<BR>\n" );
document.write( "d = distance from a to city b<BR>\n" );
document.write( "d = (rate)*(time) <BR>\n" );
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document.write( "what is known? two things:<BR>\n" );
document.write( "1. distance is same for both riders<BR>\n" );
document.write( "2. time for rider 2 is 1.5hrs longer, therefore the equation for this is:<BR>\n" );
document.write( "y = x + 1.5<BR>\n" );
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document.write( "therefore since distance is same:<BR>\n" );
document.write( "(rate rider1)*(time rider1) = (rate rider2)*(time rider2)<BR>\n" );
document.write( "(18mph)*(x hours) = (12mph)*(y hours)<BR>\n" );
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document.write( "and substitute for y since y = x + 1.5:<BR>\n" );
document.write( "(18mph)*(x hours) = (12mph)*(x + 1.5 hours)<BR>\n" );
document.write( "18x = 12(x + 1.5)<BR>\n" );
document.write( "18x = 12x + 18<BR>\n" );
document.write( "subtract 12x from both sides<BR>\n" );
document.write( "6x = 18<BR>\n" );
document.write( "divide both sides by 6<BR>\n" );
document.write( "x = 3<BR>\n" );
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document.write( "time for rider1 is 3hrs.<BR>\n" );
document.write( "time for rider2 is 3 + 1.5 = 4.5 hours<BR>\n" );
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document.write( "how far?<BR>\n" );
document.write( "d = (r)(t)<BR>\n" );
document.write( "d = (18)(3) = 54 <BR>\n" );
document.write( "distance = 54 miles<BR>\n" );
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document.write( "check by d = (r)(t) for rider 2:<BR>\n" );
document.write( "d = (12)(4.5)<BR>\n" );
document.write( "d = 54, yes--answer checks out\r<BR>\n" );
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document.write( " </SPAN>\n" );
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