CAN, COULD, BE ABLE TO

Remember that can doesn't have all the forms, only present (can) and past (could), so sometimes it is necessary to use 'be able to'.

In the present both forms are possible, though can is more common.

We use could for general ability. But if we are talking about what happened in a particular situation, we use was/were able to... or managed to... (Not could): 

They didn't want to come with us at first but we managed to persuade them. or ...we were able to persuade them, (but not 'could persuade') 

Compare: 

Jack was an excellent tennis player. He could beat anybody. (= he had the general ability to beat anybody) 

Jack and Alf had a game of tennis yesterday. Alf played very well but in the end Jack managed to beat him. or ...was able to beat him. (= he managed to beat him in this particular game) 

And now some exercises for you to practise:

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

And remember you can go to  "Grammar" to download a more accurate explanation as a document.