The BumbleBee problem

I came across a story/incident today which made me laugh but i still cannot verify the story .So if anyone has any answers then please inform me.The story is based on a famous bee problem which is often asked in Microsoft Interviews and goes something like this...

Two cars are 120 miles apart. They begin driving towards each other at 60 & 80 miles per hour respectively. A bee flies from car A towards car B at forty miles per hour. As soon as it reaches B it turns around and flies back towards A. It keeps this up until the cars collide. How far has the bee travelled?

Solution :Most people don't get that the two events ie. the movement of bee and cars are independent so you simply have to calculate the time in which the cars collide and then multiply this time with the speed of the bee.

Now the story : I have heard two versions of stories and am trying to verify which one of it is true
1 st version :The Legendary Indian Mathematician Srinivasa Ramanujan fell sick while he was in his early 30's. His condition was quite serious and chances of survival limited. At that time his friend at Trinity, G. H. Hardy used to bring him puzzles for recreation .Once he asked Ramanujan this problem to which Ramanujan replied with the answer instantly.Then Hardy told him "so you know the trick to the problem .... most people would try to use summation to solve this problem and would be stuck for ever",to which Ramanujan replied "what do you mean ,thats how i solved it."

2nd version :Again same story but this time took place between a student and Mathematician Von Neumann in his class .
So anybody knows which one is true???

[Note: After further searching i could find only one link regarding the first version which was too not authentic whereas i did found some credible links regarding second version so it may be highly probable that the second version is true.But who asked the question to Von Neumann is still not clear!! ]