The time children spend (or spends) watching TV.
The time children spend (or spends) working prevent (or prevents) then from focusing on their school work.
Could you please help on the above sentence corrections. And the explanation as well.
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For 1. , this is a subject and grammatical person problem.
The second and third person singular present-tense for verbs is generally the suffix -s
As opposed to the first person:
However the plural second and third person present-tense for verbs omits any suffix and is in the bare form:
The children run.
This resolves 1. in your question. The correct form is:
The time children spend watching TV.
For prevent vs prevents in 2., the verb is in the present-tense stative form (the verb is unchanging). Examples of this form are:
The sun shines.
He knows French.
I know German.
You know German.
Note that once again the third person has the -s suffix (while first and second person do not).
Thus in 2. , the correct form is:
The time children spend working prevents them from focusing on their school work.
N.B. It would be equally correct to say:
The time children spend working is preventing them from focusing on their school studies.
However the use of the continuous present-tense of prevent implies that this is only a problem currently and is not always a problem. The use of the stative prevents in this sentence is used to make the statement more impactful, and indicates that the problem isn't temporary.