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**The four circles represent bike 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? **

**[Problem submitted by Kevin Windsor, LACC Instructor of
Mathematics. Source: 536 Puzzles & Curious
Problems by Henry Ernest Dudeney, 1967.]**

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**Solution:**

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**A, B, C, D could ride one mile
in 1/6, 1/9, 1/12, and 1/15 of an hour respectively. They could, therefore, ride once round in 1/18, 1/27, 1/36, and
1/45 of an hour, and consequently in 1/9 of an hour (that is, 6 2/3 minutes)
they would meet for the first time.
Four times 6-2/3 minutes is 26-2/3 minutes. So, they would complete their task in 26 minutes 40 seconds past
noon (12:26:40 pm).**

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**1/18 + 1/18 = 1/9**

**1/27 + 1/27 + 1/27 = 1/9**

**1/36 + 1/36 + 1/36 + 1/36 =
1/9**

**1/45 + 1/45 + 1/45 + 1/45 +
1/45 = 1/9**