document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184017>Question 1184017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Boris and Michael are jogging around a lake. It takes Boris 6 minutes to complete a lap and<BR>\n" );
document.write( "Michael takes 8 minutes. After completing each lap, the boys take a rest, Boris for one minute<BR>\n" );
document.write( "and Michael for two minutes. Then they continue jogging. If they started jogging together,<BR>\n" );
document.write( "how long, in minutes, does it take until they are next together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814576 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52875)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Boris and Michael are jogging around a lake. It takes Boris 6 minutes to complete a lap and<BR>\n" );
document.write( "Michael takes 8 minutes. After completing each lap, the boys take a rest, Boris for one minute<BR>\n" );
document.write( "and Michael for two minutes. Then they continue jogging. If they started jogging together,<BR>\n" );
document.write( "how long, in minutes, does it take until they are next together?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem is non-standard Travel and Distance problem.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The first move/thought is to analyse it as @ankor@dixie-net.com did in his post.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;But the normal state of a person who solves it for the first time, is DO NOT BELIEVE and TO CHECK himself (or herself).\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;THEREFORE, I decided to make such a check.  My solution is below. Read it attentively.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Let make timing Table, showing time/times, when the persons, Boris and Michael, are in the starting point again,\r\n" );
document.write( "while they make their trips around the lake. In the Table, I placed timing, when they achieve this starting point and rest there.\r\n" );
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document.write( "                T     A     B     L     E    \r\n" );
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document.write( "         # of lap           1       2       3       4       5       6       7       8        9       10\r\n" );
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document.write( "        Boris' time        6-7    13-14   20-21   27-28   34-35   41-42   48-49   55-56    62-63    69-70\r\n" );
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document.write( "        Michael's time     8-10   18-20   28-30   38-40   48-50   58-60   68-70 \r\n" );
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document.write( "         # of lap           1       2       3       4       5       6       7\r\n" );
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document.write( "We look to find non-zero intersection between the given time intervals, when they rest.\r\n" );
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document.write( "Such non-zero / (non-empty) intersection is time period from 48 to 49 minutes, when Boris completed his 7-th  lap\r\n" );
document.write( "and Michael completed his 5-th lap.\r\n" );
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document.write( "<U>ANSWER</U>. First time they are next together is 48 minutes after start.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "At &nbsp;&nbsp;t = 28 minutes, &nbsp;they &nbsp;&nbsp;\" are together \" &nbsp;during the time interval which lasts &nbsp;0 minutes and &nbsp;0 &nbsp;seconds \r<BR>\n" );
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document.write( "(empty intersection of time intervals).\r<BR>\n" );
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document.write( "So, &nbsp;according to the context &nbsp;(and common sense), &nbsp;I do not consider this time moment as if &nbsp;\" they are together \".\r<BR>\n" );
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document.write( " </SPAN>\n" );
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