overyourhead

Brain Teaser Answer...
After 280 seconds, the Big Wheel would have gone round exactly 28 times, the Rotator would have gone round exactly 35 times and the Twirler would have gone round exactly 40 times.

This happens because 280 is exactly divisible by 10, 8 and 7; it is also the smallest number with that property. So they were in line again after 280 seconds, or 4 minutes 40 seconds.