Passing on a Track

Two cars (A and B) start at the starting line at the same time on a 3-mile long track, going in opposite directions.  As they drive around the course, they pass each other many times.  Exactly one hour after starting, they pass each other for the 33rd time.  At this point car A has completed exactly 20 laps.  What is the average speed of Car B?

Source: Original, based on a puzzle from Emanuel Manasci

Solutions were received from John Hewson, Jim Gillogly, Dan Dima, Joseph DeVincentis, David Bachtel, Kevin Raponi, Jeremy Galvagni, Dan Chirica, Philippe Fondanaiche, Mario Roederer, Al Zimmermann, P Giannopoulos, Jacob Samuel, Marcelo Lima, Andris Docaj, Jozef Hanenberg, Vikram Chandrasekhar, Denis Borris, Alan O'Donnell and Richard Mathar.  Most proposed methods were similar to that of Jozef Hanenberg's below:

Suppose car B would stand still on the starting line. Then car A would pass car B 20 times in one hour. Every extra passing would be the result of the driving of car B. Because they pass 33 times, car B must have completed 13 laps giving a distance of 13 x 3 = 39 miles. [and a speed of 39 mph.]

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