There are three cars driving on a track. The track is a perfect circle (circumference unknown) and is not wide enough to allow any car to pass another. Currently, the lead car is going 55 MPH and the last car is going 45 MPH. While the car in the middle is going some speed between. At this moment there is x miles between the lead car and the middle car and x miles between the middle car and the slowest car where x is not 0 or 1 miles. If the car's maintained their speed up to the point where the lead car caught the slowest car (then everyone stops), would there ever be a point and time where the distance between any two pairs is again x miles (the pairs must be x distance apart at the same time)?

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There are three cars driving on a track. The track is a perfect circle (circumference unknown) and is not wide enough to allow any car to pass another. Currently, the lead car is going 55 MPH and the last car is going 45 MPH. While the car in the middle is going some speed between. At this moment there is x miles between the lead car and the middle car and x miles between the middle car and the slowest car where x is not 0 or 1 miles. If the car's maintained their speed up to the point where the lead car caught the slowest car (then everyone stops), would there ever be a point and time where the distance between any two pairs is again x miles (the pairs must be x distance apart at the same time)?

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