.
The key to the problem' solution is that
Joan passes Jim every time, when he covers one circumference more distance than Jim.
Solution
Joan runs 
of the circular track length in one minute.
Jim runs 
of the circular track length in one minute.
Every minute, the distance between Joan and Jim increases by - of the track length.
// assuming the distance is measured along the circumference in the same direction as they run.
- = - 
= 
- = 
= 
of the track length.
Hence, every 5 minutes Joan covers 1 track's circumference length more than Jim.
Making one circumference length more is exactly the condition for Joan to pass Jim.
Hence, the answer to the problem is 5 minutes.
Again, the answer to the problem is x= 5 minutes.
Solved.
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Those who have enough brain cells in their heads, MOMENTARILY will see analogies between the given problem and
the "joint work problem", when one pipe fills the tank, while the other pipe "drains" it.
