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" );
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document.write( "The next time the two are together will be when Boris has run one lap more than Michael.  That might happen when they are both resting; or it might happen when both are jogging.<br><BR>\n" );
document.write( "Since the ratio of the times it takes them to run a lap is 6:8 = 3:4, the first time they are together again should be near the time that Boris completes 4 laps and Michael completes 3.<br><BR>\n" );
document.write( "So look at the times around the time when Boris completes 4 laps and Michael completes 3.<br><BR>\n" );
document.write( "Boris' \"cycle\" is 7 minutes long.  He completes the rest after his 4th lap at 28 minutes, which means he finished his 4th lap at 27 minutes.<br><BR>\n" );
document.write( "Michael's cycle is 10 minutes long.  He completes the rest after his 3rd lap at 30 minutes, which means he finished his 3rd lap at 28 minutes.<br><BR>\n" );
document.write( "So the two boys are next together at 28 minutes, when Michael has just finished his 3rd lap and Boris is just finishing the rest after his 4th lap.<br><BR>\n" );
document.write( "ANSWER: 28 minutes<br><BR>\n" );
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