You traveled three hours at a certain speed. If you had taken 1 minute less to do each mile you would have gone 30 miles farther than you actually did.
How far did you go?
The distance is 60 miles.
The trick is to realize that v1 + 10 mph = v2, and at what point does the interesting function "1 minute less to do each mile" create an increase of 10 mph or 1m/6min. The only possible speed that this occurs is 20 mph which makes v2 = 30 mph.
I say this is an interesting function because it increases exponentially until 60 mph, and it decreases exponentially from to 60. I suppose if you were doing 60mph and then started taking a minute less to do each mile, you would quickly disproove Einstien's theory of relativity!
I re-edited this comment to try to explain my line of thinking more clearly. I hadn't realized that this solution was a little bit different from the others posted.
Michael
Edited on November 30, 2004, 5:56 am