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Hi everybody, I have two doubts.

1. In this sentence:

Many championship automobile and motorcycle races take place in Daytona Beach, Florida.

If the phrase "championship automobile and motorcycle" describes "races".

That is to say it would mean: races of championship automobile and motorcycle.

2. In this other sentence:

In typical pioneer settlements, men, women, and children worked from morning until night at farm and household tasks.

If the phrase "farm and household" describes "tasks".

That is to say it would mean: tasks of farm and household.

Thanks a lot for your help.
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I have two doubts questions.

Many championship automobile and motorcycle races take place in Daytona Beach, Florida.

=~ Many championship automobile races and championship motorcycle races take place ...

=~ Many championship races for automobiles and championship races for motorcycles take place ...

____

at farm and household tasks.

=~ at farm tasks and household tasks.

=~ at tasks related to work on a farm and tasks related to work in a house

___

If your native language uses an "of" phrase to express these concepts, then yes, translated literally from your language, the "of" phrase captures the meaning. However, in English we would never use these phrases:
races of championship automobile and motorcycle
tasks of farm and household.

CJ
Comments  
This not very clear cut, but I would say no to both your doubts.
1. "championship automobile and motorcycle" describes "races". Yes, it is the type of races held there, they are Championship races for automobiles and motorcycles.
but to say "races of championship automobile and motorcycle" is slightly different. Here you are saying races containing championship automobiles and motorcycles. And yes, it would have to be in the plural. And it infers that the vehicles have to be championship vehicles to qualify. Whereas in the first, the races are to determine the champions.
You could say "championship races of automobiles and motorcycles"
2. similarly to 1. "tasks of farm and household" doesn't work. You could say "tasks of farm and household duties".
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 CalifJim's reply was promoted to an answer.
" Many championship automobile races and championship motorcycle races take place "
" at farm tasks and household tasks ".

These are the answers I was looking for, thank you. Also, I understood the thing about "of".

And now, for example, in the phrase "at farm tasks and household tasks", how it was reduced to this "at farm and household task". Is there any grammatical rule or something?
doesxpIs there any grammatical rule or something?
I suppose you might call it a rule.

Any two constituents of a sentence that have the same status can be combined with and.

Here you have two cases of a noun used as an adjective (describing tasks), so you can combine them as seen in your example.

Here are a few other examples.

indoor clothing and outdoor clothing > indoor and outdoor clothing
gas storage tanks and oil storage tanks > gas and oil storage tanks
Italian flags and German flags > Italian and German flags
formal wear and casual wear > formal and casual wear

Sometimes both is added at the beginning:

bold children and timid children > both bold and timid children
cheerful songs and sad songs > both cheerful and sad songs

Is that the "rule" you wanted? Emotion: smile

CJ
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Yes, it is [Y]. Great answer, thank you so much.