I inquired whether the airplane would arrive on time.

Literal

Airplane [subject-が] on-schedule [at-に] arrive [whether or not-かどうか] inquired.

~かどうか ('whether or not') embeds a yes/no question as the object of a verb. 定刻 (ていこく) means 'scheduled time, on time.' 問い合わせる is a compound verb meaning 'to inquire, make an inquiry.'