I think the 1 hr answer is correct;

the other argument of 10 minutes, is a bit off. They are failing to realize the ground being made up by car B is only .17 mile per minute.

60/60 = 1 mile per minute
50/60 = .83 mile per minute.

1 - .83 = .17.
.17 x 60 minutes = 10.2 miles.


maybe I'm wrong though.

Rounding error. 50/60 = 0.83333333....

Therefore, 1 - 0.8333333..... = 0.166666666...

One hour, minus the effects of relativity.

You know that Car B will pass Car A at some point and will never again be caught. You also know that in one hour they will be at the same point, so therefore...

Hmm... good point. I would say somewhere between 1 hour and 59 minutes, 59.9999999999999 seconds, depending on if you are standing nearby watching or in one of the cars.