This is a puzzle from Boris Kordemsky’s 1972 Moscow Puzzles.

“Four cyclists do their act on circular paths, each 1/3 mile long. They start simultaneously at the black spots, with speeds of 6, 9, 12, and 15 miles per hour.  By the end of the act (20 minutes), how many times will they have simultaneously returned to the spots where they started?”

Answer.

See Bicycle Figures Riding for solutions.