Three friends A, B and C regularly jog in circular jogging track every morning. The track is 1000 m in circumference.
A takes 8 mins to complete one lap, B takes 10 mins and 40 secs and C takes 12 mins. One day they decided to find out if they set out together in the same direction from a point what would be the fastest time for all of them to meet at any point on the track. What did they conclude?
The second day C decides to run in the opposite direction from the starting point. When will they all meet? Will this be sooner than the time taken on day one? Where do they meet in both cases?
I was hoping for some kind of interesting intersection a a point besides the starting point. I made a graph using geometer's sketchpad and found two places when they do come close to having a three way meeting in the first 5760 seconds.
C passes A at 2016 seconds at the 200m mark. C continues and passes B at 2032.94 seconds at the 176.47m mark.
Well, 24 meters on a 1000 meter track is pretty close. There is another symmetrical near miss an equal distance from the end.
Posted by Jer
on 2006-04-13 13:38:00