How would you deal with these scenarios in a lowish stakes cash game?
A: You have asp kh in mid position. You make your standard raise pre flop which is called by the button only.
Flop comes:

js. You decide to make a continuation bet of about half the pot and he calls.
How do you proceed on the turn, assuming the turn misses you?
B: You have tc td in late position. You call a raise from mid position and the two of you see a flop of:

.
He makes a continuation bet of about half the pot - how do you play it from there?
You have no read on either players' style of play.
Really interested in people's opinions of how to play these two scenarios - I find them some of the hardest things to deal with.