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# help

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The four circles represent cinder paths. The four cyclists started at noon. Each person rode round a different circle, one at the rate of six miles an hour, another at the rate of nine miles an hour, another at the rate of twelve miles an hour, and the fourth at the rate of fifteen miles an hour. They agreed to ride until all met at the center, from which they started, for the fourth time. The distance round each circle was exactly one-third of a mile. When did they finish their ride?

Jan 6, 2020

#1
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It takes the cyclist of 6 mph 10/3 minutes for 1 lap.
It takes the cyclist of 9 mph 20/9 minutes for 1 lap.
It takes the cyclist of 12 mph 5/3 minutes for 1 lap.
It takes the cyclist of 15 mph 4/3 minutes for 1 lap.

The LCM [10/3, 20/9, 5/3, 4/3] = 20/3 = 6 2/3 minutes when all four will meet at the start for the first time.
By the way, when they meet the first time, they will have done:2, 3, 4, 5 laps each respectively.
6 2/3 x 4 =26 2/3 minutes after noon hour when they will all meet for the 4th time.

Jan 6, 2020

#1
+1

It takes the cyclist of 6 mph 10/3 minutes for 1 lap.
It takes the cyclist of 9 mph 20/9 minutes for 1 lap.
It takes the cyclist of 12 mph 5/3 minutes for 1 lap.
It takes the cyclist of 15 mph 4/3 minutes for 1 lap.

The LCM [10/3, 20/9, 5/3, 4/3] = 20/3 = 6 2/3 minutes when all four will meet at the start for the first time.
By the way, when they meet the first time, they will have done:2, 3, 4, 5 laps each respectively.
6 2/3 x 4 =26 2/3 minutes after noon hour when they will all meet for the 4th time.

Guest Jan 6, 2020