I was practicing translating the following sentences:
Relax, this problem has already been solved! 放輕鬆吧，這個問題已經解決了。
That foreigner hasn’t taken a bus for a long time. 那個外國人很久沒有搭巴士了。
I feel I added 了 at the end of each sentence based on feel but am unsure why. If I omitted 了 would the sentences still be correct? What meaning is added by 了 in this case?