To Catch Up With
To Overtake, To Keep Up With
intransitive verb, godan verb
To follow then attach yourself to the whoever you're following is to catch up with someone.
おいつく
The readings are the ones you learned with the kanji, but you can also just notice that this word includes 追う and 付く combined.
前日にシアトルまでと歩で出発したコウイチに車で五分もかからず追い付きました。
We took a car and less than five minutes later we overtook Koichi who had departed for Seattle on foot on the previous day.
100メートル走でクリステンに追い付くことができたらオリンピックに出られるよ。
If you can catch up with Kristen in the hundred meter dash, you can compete in the Olympics.
トーフグの塗り絵は人気すぎて、生産が需要に追い付かなかった。
Tofugu’s coloring book was so popular that production couldn’t keep up with demand.