On a bypass engine does the bypass air travel faster or slower than core air? Using the convergent /divergent duct theory the low pressure cold stream bypass air would travel faster but I read on a web page that the bypass air travels much slower than core air. But again using the convergent / divergent duct theory core air is subject to higher pressures and temperatures therefore should theoretically travel slower?

Or is it because air is mixed with fuel and accelerated during combustion which makes the core speed faster and Bernoulli converging / diverging duct theory I stated above doesn't apply? 

Hopefully someone can tell me if I'm thinking this incorrectly... Simple explanation please and not something over complicated.

Thanks!
The simple way to think of it is the bypass engine is kind of part way between a pure jet and a turboprop.   In a nutshell, the pure jet moves a little bit of air a lot; the turboprop's propeller moves a lot of air a little, relatively.  In other words, small mass at high velocity vs large mass at low velocity, to get the same push.  

A bypass jet engine is somewhere in between.  It's just a fixed pitch non-geared turboprop with 30 or 40 blades, in a shroud, instead of 3 or 4 variable pitch blades in the open (geared turbofans get even closer to the "fixed pitch turboprop" thing).   

The package of air being accelerated is smaller than a propeller, but much larger than a pure jet, so fan's exhaust velocity is also in between; faster than the wash of a propeller, slower than the exhaust of the core.