A day goes by quickly, but a week also goes by really quickly.
"A day goes by quickly"＝「一日が経つのはとても早い」
"but a week also goes by really quickly"＝「でも、一週間が経つのもとても早い」
Sentence in context:
"The older I get, not only do I feel that a day goes by quickly, but that a week also goes by really quickly."
The days fly by, and so do the weeks.
1日終わるのは早いけど、1週間も本当にあっという間です。
time flies のように fly を使って「時間があっという間」をよく表します。
他には
Time goes by so fast.
Time goes by so quickly.
アメリカ合衆国 
