Can, could and be able to

We use can to say that something is possible or that somebody has the ability to do something. We use can + infinitive (can do / can see etc.):

We can see the lake from our bedroom window.
Can you speak any foreign languages?
I can come and see you tomorrow if you like.

The negative is can’t ( = cannot ):

I’m afraid I can’t come to the party on Friday.

Be able to…is possible instead of can, but can is more usual:

Are you able to speak any foreign languages?

But can has only two forms, can (present ) and could (past ). So sometimes it is necessary to use be able to… Compare:

I can’t sleep. but  I haven’t been able to sleep recently. (can has no present perfect )
Tom can come tomorrow. but  Tom might be able to come tomorrow. (can has no infinitive )

Could  and was able to…

Sometimes could is the past of can. We use could especially with :

see  hear  smell  taste  feel  remember  understand

When we went into the house, we could smell burning.
She spoke in a very law voice, but I could understand what she said.

We also use could to say that somebody has the general ability or permission to do something:

My grandfather could speak five languages.

We were completely free. We could do what we wanted. ( = we were allowed to do…)

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 ):

The fire spread through the building quickly but everybody was able to/managed to escape. (but not ‘could escape’ )

They didn’t want to come with us at first but we managed/were able to persuade them. (but not ‘could persuade’ )

The negative couldn’t ( could not ) is possible in all situations:

My grandfather couldn’t swim.

We tried hard but we couldn’t persuade them to some with us.

He played well but he couldn’t beat her.