-- The circumference of the track is (2 · π · radius).
Circumference = (2 · π · 1.67m) = 10.49 meters .
-- The train's speed is (31.5 cm) / (10.49 m) of the track's circumference, per second. That's ...
(31.5 cm) · (1m / 100cm) / (10.49 m / circumference) =
(31.5 / 100 · 1,049) (cm · m / cm · m) =
= 0.030 of the circumference per second.
The train performs 0.03 revolution per second.
It takes (1/0.03) = about 33.3 seconds to complete one revolution of the track.