Mind-Boggler:
New York and New Jersey are approximately 70 miles apart. I drive from NY to NJ at 70 mph. How fast must I then drive back from NJ to NY in order to double my average speed for the whole journey?
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Mind-Boggler EXPLAINED:
The answer is that this is not possible!
This may seem counter-intuitive, but it is actually possible to prove this!
I have covered 70 miles in one hour in the first part of my journey. This makes my average speed 70 mph. To double this, my average speed needs to be 140 mph. But here lies the problem! When I have finished both parts of my journey, I will have ridden a total of 70 x 2 = 140 miles. Since I need to have an average speed of 140 mph and I have to travel 140 miles, my total driving time must be 1 hour. This is not possible as I have already driven for 1 hour, which means that I have no time left for the journey back. Thus, this boggler has no solution.