Earth is about 25,000 miles around the equator.  The continents were all packed 
together as "Pangaea" about 250 million years ago.  So I estimate that a typical 
continent has moved halfway around the world (12,500 miles) since the time of 
Pangaea.  So that's a speed of

v = 12,500 mi/ 250,000,000 yr = 0.00005 miles per year.  

At that slow rate, it's not really sensible to compute the speed in miles per hour 
- it'd be such a small number, there's no good reference.  So let's try inches per 
year:

v = 0.00005 mi/yr * 5280 ft/mi * 12 in/ft = 3.168 inches per year

Again, since I've been using "numerical common sense" to estimate my numbers, 
keeping more than one or two decimal places would be adding false precision.  So I 
estimate that the continents are moving 3 inches per year.  (This means, by the 
way, that trans-Atlantic phone cables need to be lengthened every few years!)

This answer, and the way I arrived at it, may seem way too simplistic.  Am I 
really close to the right answer?  Well, according to a page at the U. S. 
Geological Service website:

"Pangaea broke up and gave birth to the Atlantic Ocean, which has been widening a 
few inches a year ever since, crowding our side of North America toward the 
Pacific."

In other words, this simplistic calculation is right on target!