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Mary can speak English quite well but she can’t write it at all (can = to be able, to know how to...).
John can keep a secret if he wants to (can = to be capable of).
I can drive a car = I know how to...
I couldn’t understand him when he spoke very fast (= was unable to, was incapable of...).
He could (was able to) speak English very well when he was twelve.
The meaning of ability is expressed only by “to be able to” when the reference is to the future, as can,
having no infinitive, has no future tense form.
Soon he will be able to speak English quite fluently.
Can is interchangeable with to be able to when it denotes mere capacity,
I couldn’t/was not able to do that new job; it was too difficult.
This man could/was able to cure all diseases.
But only to be able to is used to express attainment or achievement of something through some capacity.
Thus
to be able to often combines the idea of “ability” and “achievement”. In this case was able to means
“managed to” or “succeeded in”, and could is impossible.
The fire brigade was able (succeeded in putting, managed) to put out the fire before it destroyed the other
buildings. Пожарные сумели, им удалось ...
I was able to go to the mountains yesterday as I had a day off (I could and went).
I was able to finish my work in an hour (I managed, I could and did it).
2. Possibility.
a) possibility due to circumstances:
Anybody can make a mistake. Ошибаться может каждый.
You can hardly blame him for that. Вряд ли можно его за это винить.
I couldn’t take your coat without paying you for it.
b) possibility due to the existing rules of laws:
In old days a man could be sentenced to death for a small crime. В старые времена можно было
приговорить человека к смерти за небольшое преступление.
The Lower House alone can initiate financial measures. Только Палата представителей может
выносить на рассмотрение финансовые вопросы.
c) possibility of the idea (the so-called “theoretical” possibility):
The railways can be improved. (It is possible for the railways to be improved, as they are not yet
perfect.)
In general statements of possibility can has roughly the same meaning as “sometimes”.
The sea can be rough. = The sea is sometimes rough. Mope иногда бывает бурным.
Can is generally used in questions about possibility and in statements about impossibility.
Can this be true? (Is it possible that this is true?) Неужели это правда?
This can’t be true. (It is impossible that this is true.)