Henry Ernest Dudeney/Puzzles and Curious Problems/69 - The Four Cyclists

Puzzles and Curious Problems by Henry Ernest Dudeney: $69$

The four circles represent cinder paths.

The four cyclists started at noon.

Each person rode round a different circle,

one at the rate of $6$ miles an hour,

another at the rate of $9$ miles an hour,

another at the rate of $12$ miles an hour,

and the fourth at the rate of $15$ miles an hour.

They agreed to ride until all met at the centre, from which they started, for the fourth time.

The distances around each circle was exactly one-third of a mile.

When did they finish their ride?

1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Locomotion and Speed Puzzles: $69$. -- The Four Cyclists
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Speed & Distance Puzzles: $83$. The Four Cyclists