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かかるだろう

will take

→ 掛かる
phrase Common #7,040
will take Used to predict how much time something will require; だろう adds a sense of probability.
JA: この作業には三時間かかるだろう。
EN: This work will take three hours.

彼がよくなるにはしばらくかかるだろう。

It will probably take him a while to get better.