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に追いつくでしょう

will catch up with

→ に
phrase Rare #33,909
will catch up with Used to predict that someone or something will catch up to a person or reach the same level as something. でしょう makes the statement sound like a prediction or expectation.
JA: このペースなら、すぐに先頭の選手に追いつくでしょう。
EN: At this pace, we will soon catch up with the leading athlete.

もし君が急げば、すぐに彼女に追いつくでしょう。

If you hurry, you'll catch up with her soon.

すぐ出発しなさい、そうすれば彼らに追いつくでしょう。

Leave immediately, and you’ll catch up with them.

彼はすぐにトムに追いつくでしょう。

He will catch up with Tom soon.

急げば彼に追いつくでしょう。

If you hurry, you'll catch up with him.

供給がまもなく需要に追いつくでしょう。

Supply will soon catch up with demand.