document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106402>Question 1106402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A piece of land is 20 miles in circumference. Three persons, A, B, and C, start from the same place and travel the same way. A travels 3 mph, B 7 mph, and C 11 mph. In what time will they be together again?\r<BR>\n" );
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document.write( "Unsure how to solve.  Non-homework.<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 #721372 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=721372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It takes 20/3 hours for the first to go around, 20/7 for the second and 20/11 for the third.<BR>\n" );
document.write( "Look at the first and second<BR>\n" );
document.write( "3/20 of the circumference is the distance the first goes around in an hour.<BR>\n" );
document.write( "How long until A is lapped by the second, who goes around 7/20 of the circumference in an hour?<BR>\n" );
document.write( "(3x/20)+1=(7x/20) is the distances traveled in one hour, adding a lap to the A to have them both meet again.<BR>\n" );
document.write( "multiply everything by 20<BR>\n" );
document.write( "3x+20=7x, 4x=20, x=5<BR>\n" );
document.write( "In 5 hours, the first goes 15/20 or 3/4 of the way, and the second goes 35/20 around or 1 3/4 of the way.  They meet.<BR>\n" );
document.write( "If the first meets the second, what about the second and the third?<BR>\n" );
document.write( "(7x/20)+1=(11x/20)<BR>\n" );
document.write( "7x+20=11x<BR>\n" );
document.write( "4x=20<BR>\n" );
document.write( "x=5 hours as well.<BR>\n" );
document.write( "In 5 hours, C goes 55/20 around, and that is 2 15/20 laps or 2 3/4 the way.  The three of them will meet in 5 hours, 3/4 of the way around the track.<BR>\n" );
document.write( "(One can do this for the planets as well).\r<BR>\n" );
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document.write( "Another way in x hours A goes (# of laps) 3x/20 miles, B 7x/20 miles, and C 11x/20 miles<BR>\n" );
document.write( "B and C have to go at least 1 lap more than A.<BR>\n" );
document.write( "7x/20 -1=3x/20<BR>\n" );
document.write( "4x/20=1<BR>\n" );
document.write( "x=5<BR>\n" );
document.write( "Try that for C.<BR>\n" );
document.write( "11x/20-1=3x/30<BR>\n" );
document.write( "8x=20<BR>\n" );
document.write( "x=2.5.  C laps A in 2.5 hours and every 2.5 hours.<BR>\n" );
document.write( "Try C and B<BR>\n" );
document.write( "11x/20-1=7x/20<BR>\n" );
document.write( "4x/20=1<BR>\n" );
document.write( "x=5 hours.<BR>\n" );
document.write( "C laps B in 5 hours and A in 2.5 and 5 hours, so they are all together in 5 hours. </SPAN>\n" );
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