Question 1184017
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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>
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>
So look at the times around the time when Boris completes 4 laps and Michael completes 3.<br>
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>
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>
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>
ANSWER: 28 minutes<br>