Which country gets ill every time?

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 easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

What is the fastest way to double your money?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

What part of the chicken has the most feathers?

I am a number I am not an odd number I am higher than 90 I am not higher than 100 If you subtract me from 100, you get nothing. What number am I?

A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

1) Suppose the lion is hungry, will he be able to eat up the tamer?
2) If yes, how long can the tamer survive?

Buy me, smell me or deliver me, I do not change.

Who am I?

A new Engineering building containing 100 offices had just been completed. John was hired to paint the numbers 1 to 100 on the doors. How many times will John have to paint the number nine (9)?