Roads in town looks like this:
Where $t=45$ means the path takes 45 minutes, and $t=\frac{N}{100}$ means the path takes as many minutes as the number of drivers who chose that path divided by $100$. For example, if $200$ drivers go from home to B, that path takes $\frac{200}{100}=2$ minutes.
Every day, $4000$ drivers leave home, heading for work. Whenever there is a choice between two paths, every driver will choose the shortest path.
What is the average commute time, in minutes, from home to work?
Solution: Initially both the path costs same time (N=0, hence 45 minutes). Now since A is taken by one driver it costs (45+1/100) So next driver will take path B which has still t=45+0/100, therefore he will take that path. So on so forth,
$$ T(A) = 45+45+1/100+45+2/100+...+45+1999/100$$
T(B) will be same as T(A). Therefore solving this summation we get Avg commute time as 54.995 minutes .
What's wrong in this analysis? P.S. this question is form Expii-Travel
Edit: So correct answer is 65, 45+ N/100 i.e. $$T(A)=T(B)=45+2000/100=65$$ The problem is poorly stated and assumed reader to assume somethings. But if asked to do analysis in the above stated manner then would it be correct?