document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1000288>Question 1000288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two man cycled towards each other distance of 200 km ,one from A and other from B.the first tourist left point A 6 hrs later than the 2nd left pt B,  reached at same time find speed of faster </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #617756 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=617756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE SITUATION AS PER MY INTERPRETATION OF THE WORDING:<BR>\n" );
document.write( "The first tourist left point A, cycling towards point B, 6 hrs after a second tourist had left point B cycling towards point A. Both tourists reached their destination at the same time. The distance between points A and B is 200 km.\r<BR>\n" );
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document.write( "CONCLUSIONS:<BR>\n" );
document.write( "The first tourist cycled at a faster average speed than the second tourist.<BR>\n" );
document.write( "We do not have enough information to calculate the average speed of the first, faster tourist. (We cannot calculate the average speed of the second, slower tourist either).\r<BR>\n" );
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document.write( "EXPLANATION:<BR>\n" );
document.write( "There are infinity of mathematically possible (although not necessarily plausible) answers.<BR>\n" );
document.write( "We define variables like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B1%5D ALIGN=MIDDLE  ALT=\"v%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= average speed of the first tourist, in km per hour,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B2%5D ALIGN=MIDDLE  ALT=\"v%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= average speed of the second tourist, in km per hour, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >= time the first tourist spent cycling from A to B, in hours.<BR>\n" );
document.write( "From the wording of the problem we know that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2B6 ALIGN=MIDDLE  ALT=\"t%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >= time the second tourist spent cycling from B to A, in hours,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Av%5B1%5D=200 ALIGN=MIDDLE  ALT=\"t%2Av%5B1%5D=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >= distance cycled by the first tourist, in km, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%2B6%29%2Av%5B2%5D=200 ALIGN=MIDDLE  ALT=\"%28t%2B6%29%2Av%5B2%5D=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >= distance cycled by the second tourist, in km.<BR>\n" );
document.write( "Unfortunately, the system of equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28t%2Av%5B1%5D=200%2C%28t%2B6%29%2Av%5B2%5D=200%29 ALIGN=MIDDLE  ALT=\"system%28t%2Av%5B1%5D=200%2C%28t%2B6%29%2Av%5B2%5D=200%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with 3 variables related by only 2 equations,<BR>\n" );
document.write( "has an infinite number of solutions.<BR>\n" );
document.write( "We can tabulate some of them:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%288%2C4%2C%0D%0At%2Ct%2B6%2Cv%5B1%5D=200%2Ft%2Cv%5B2%5D=200%2F%28t%2B6%29%2C%0D%0A2%2C8%2C100%2C25%2C%0D%0A4%2C10%2C50%2C20%2C%0D%0A5%2C11%2C10%2C18%262%2F11%2C%0D%0A8%2C14%2C25%2C14%262%2F7%2C%0D%0A10%2C16%2C20%2C12.5%2C%0D%0A14%2C20%2C14%262%2F7%2C10%2C%0D%0A16%2C22%2C12.5%2C9%261%2F11%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Maybe the first tourist was Superman, and cycled for only 4 hours at 50 km per hour,<BR>\n" );
document.write( "while the second tourist was a Tour de France pro, and covered the same 200 km in 10 hours, at a remarkable average speed of 20 km per hour.<BR>\n" );
document.write( "Maybe the first tourist was that Tour de France pro, who covered the 200 km from point A to point B in 10 hours, at an average speed of 20 km per hour,<BR>\n" );
document.write( "and the second tourist was an endurance athlete who managed to cover the same 200 km in 16 hours, at an average speed of 12.5 km per hour.<BR>\n" );
document.write( "Since the possibilities are infinite, I cannot list or describe them all.<BR>\n" );
document.write( "I just tabulated a few possibilities, and described only two. </SPAN>\n" );
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