Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?
As per the question, the middle car is running right now approximately at 50 MPH. Therefore, with time, the distance between them will keep increasing by x miles every hour for a certain time. After that, it will start decreasing between the leading car and the last car till they meet.
Therefore, you will find no point where the distance between the cars is x miles again.