Why is it ほかのことに気を取られているうちにご飯を食べる時間がなくなってしまった and not ほかのことに気を取られたうちに……; i.e. why use the continuous verb tense rather than the past tense for the first phrase of the sentence?
The phrase before うちに indicates the general time during which an action or state occurs, relative to the main action. As a result, it never uses the past tense even if the main clause does, unlike in English. Compare, for example, the following sentences:
彼女はいつも寝ているうちに出ます。 = She always leaves while I am sleeping.
彼女は昨日寝ているうちに出ました。 = She left yesterday while I was sleeping.
Only the main verb changed tense in Japanese, while both changed in English.
The phrase before うちに indicates the general time during which an action or state occurs, relative to the main action. As a result, it never uses the past tense even if the main clause does, unlike in English. Compare, for example, the following sentences:
彼女はいつも寝ているうちに出ます。 = She always leaves while I am sleeping.
彼女は昨日寝ているうちに出ました。 = She left yesterday while I was sleeping.
Only the main verb changed tense in Japanese, while both changed in English.