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I was wondering if anyone had a clear and easy to understand description of the difference between the meaning of the verb "poder" as used in the preterite tense versus in the imperfect tense (both affirmative and negative).

Here is an example that I find very confusing:

I was given the sentence in an exercise in my textbook:

Sí, los jugadores no ___ terminar el partido. Empezó a llover y no paró hasta la medianoche. Y tú, ¿por qué no estuviste?

and I was asked to fill in the blank with etiher podían (imperfect) or pudieron (preterite). I have read from various places that "no podían" means "they weren't able to/they couldn't" while "no pudieron" means "they tried and failed".

The answer turns out to be "pudieron", but I am not sure why. It makes sense that the players tried to finish their game but "failed" due to the rain, but it also makes sense to be that the players simply weren't able to or couldn't because of the rain. I feel that this sentence can be interpreted in multiple ways, so both answers are technically correct. However, the textbook had the answer set on "pudieron" so I suspect there may be an intricate detail that I am overlooking that makes "pudieron" make more sense than "podían".

Could anyone help me out? Also other examples and affirmative examples with "poder" would be appreciated.

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The difference between preterite and imperfect has to do with the manner of describing a situation, either from the point of view of the end result or the process. As Guifa says in his answer, poder specifically means mere capability when in the imperfect; it means achievement when in the preterite.

No pudieron terminar means they were (after some time) unable to finish, and the speaker is explaining the end result: no achievement. No podían terminar means they were (presumably) trying to finish, and failing, and the speaker is focusing on this process.

Imagine we're talking about a dessert.

  • If I was so full I just couldn't finish my dessert, I would describe the final situation by saying: No pude terminar el postre. So the dessert is or was presumably still there partly untouched, and that's the end of the story.

  • But if was interrupted e.g. by someone calling me on the phone, then someone knocking on my door, etc., so that in the end I just couldn't finish eating because I had to go, I would later describe the ongoing situation at that time by saying: No podía terminar el postre. The story might continue at that point. If not, the hearer would probably eventually ask: Y al final, ¿pudiste terminar el postre?, because the imperfect leaves room for doubt.

Truly, in the example you gave, you could have used the imperfect, but the context strongly suggests otherwise; if you used the imperfect, the story would sound unfinished. So they were at a given time unable to finish, and it rained a lot, and? Did they finally manage to finish? Did they wait until after midnight and resume playing?

Examples with affirmative poder, let's see:

  • Al llegar a la cima pudieron ver claramente el pueblo en el fondo del valle. "When they came to the top, they could clearly see the town at the bottom of the valley." Meaning: they climbed up to the top, and became (more or less suddenly) able to see something they had up till then unable to see. They achieved something (the seeing) and that was it.
  • Mientras subían desde el valle podían ver de a ratos el río. = "As they climbed up from the valley they could see the river from time to time." Meaning: as they climbed, they were on-and-off able to see the river. We don't know if, at the end of the climb, they were still able to see it.

Another one:

  • Podían sentarse donde quisieran. = "They could sit wherever they wanted." They were able and permitted to sit whenever they wanted; this is a fact about their ability to choose any place. (Note the subjunctive quisieran.)
  • Pudieron sentarse donde querían. = "They could (were allowed to) sit wherever they wanted." They were able and permitted to sit anywhere, and did; this is fact about their final choice of seats. (Note the indicative querían.)
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  • Thanks for the detailed answer. So it looks like in general the imperfect (podían, etc.) leaves room for doubt (e.g. did they actually finish the game?) so that’s why the preterite should be used. – Max Mar 26 '18 at 11:55
  • Well, it's not doubt, it's incompleteness (the essence of the imperfective tenses). But that's about it. – pablodf76 Mar 26 '18 at 15:09
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Poder in the imperfect expresses a mere capability, irrespective of any concrete situation.

The preterite is used to describe concrete single actions (hence the tried and failed sense), but it is also use to focus on the beginning or end of actions (conocí a Julia "I met Julia", that is, the start of my knowing her, afterwards, conocía a Julia "I knew her").

In this case, there is a clear beginning to their inability and that beginning is relevant. We're not concerned with a general inability to finish the game, rather when that inability began.

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an easy explanation between the difference between the perfect and imperfect past(preterit) is :

Perfect: is something that already happened in a defined moment

Imperfect : is something that happened continuously in the past and might or might not have finished.

examples

Perfect : Yo pude levantar esa piedra

I was able to lift that stone, (but only happened once)

Imperfect : yo podia levantar esa piedra

I was able to lift that stone, (but this is something that happened a lot of times in the past and also i might be able to do again if i try)

the verb "poder" is hard to translate to english, lets try the previous examples without the verb poder

Yo levante esa piedra

i lifted that stone

yo levantaba esa piedra

i used to lift that stone

As you cannot conjugate the verb "can"(poder) with the "used to" , it becomes...complicated

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I will give you some paradigms.

The imperfect describes the scene -- the ongoing action. The preterite, or simple past, reports facts that occurred at a specific point on the timeline, as a newspaper reporter might do.

Preterite example à la newspaper report:

Los jugadores no pudieron terminar el partido. | The players could not finish the game.

Imperfect: Let's set the scene with the imperfect and then put some interesting action in the foreground with the preterite:

Hacía sol y nuestros muchachos jugaban de maravilla, mejor que nunca. Pero de pronto empezó a llover a cántaros. No terminaron de jugar el partido. | It was sunny and our boys were playing marvelously well, better than ever. But suddenly it started to rain cats and dogs. They didn't finish playing the game.

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