SOLUTION: Ann, Beth, and Cathy start walking from the same place counter clockwise around a circular track with length 300 meters. Ann walks 120 meters/min, and Beth walks 100 meters/min, an

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Ann, Beth, and Cathy start walking from the same place counter clockwise around a circular track with length 300 meters. Ann walks 120 meters/min, and Beth walks 100 meters/min, an      Log On


   

Question 1163720: Ann, Beth, and Cathy start walking from the same place counter clockwise around a circular track with length 300 meters. Ann walks 120 meters/min, and Beth walks 100 meters/min, and Cathy walks 70 meters/min. In how many minutes will three of them meet again?
Answer by ikleyn(52787) About Me  (Show Source):
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The difference of rates  Ann-Beth  is 120-100 = 20 m/min.

It means that  Ann and Bet will meet every 300/20 = 15 minutes somewhere on the circular track.



The difference of rates  Ann-Cathy  is 120-70 = 50 m/min.

It means that  Ann and Cathy will meet every 300/50 = 6 minutes somewhere on the circular track.



Now you take the Least Common Multiple of the integer numbers  15 and 6, which is 30.



It is your ANSWER:  three of them will meet every 30 minutes.



The first meeting point is  at the distance 120*30 = 3600 m for Ann;  100*30 = 3000 m for Beth  and  70*30 = 2100 m for Cathy,

but, although the distances along the circumference are different, they do represent the same point on the circular track, geometrically.



Notice that this meeting point is the same point they started from.

Solved and explained.