
weiterkommen
to get ahead
To make progress in an activity, a project, or in personal or professional development.
Ich lese dieses Fachbuch, um in meinem Beruf weiterzukommen.
I'm reading this specialist book in order to get ahead in my career.
to get ahead / progress
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to get ahead
To make progress in an activity, a project, or in personal or professional development.
Ich lese dieses Fachbuch, um in meinem Beruf weiterzukommen.
I'm reading this specialist book in order to get ahead in my career.

to advance
To reach the next stage or round in a competition, exam, or selection process.
Unsere Mannschaft hat das Viertelfinale gewonnen und ist somit eine Runde weitergekommen.
Our team won the quarterfinal and has therefore advanced one round.

to make progress
To find a solution to a problem or difficult task, or to receive the necessary help in order to continue.
Ich komme bei dieser Matheaufgabe einfach nicht weiter, kannst du mir helfen?
I just can't make any progress on this math problem; can you help me?
'Weiterkommen' (to get ahead / progress) is a separable verb. The prefix 'weiter-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Mit diesem Plan kommen wir sicher weiter.
With this plan, we'll definitely make progress.
The perfect tense of 'weiterkommen' (to get ahead / progress) is always formed with the auxiliary verb 'sein' (to be), because it describes a form of movement or development. So you say 'ich bin weitergekommen' (I have made progress / I got ahead).
Bist du mit deiner Arbeit schon weitergekommen?
Have you made any progress with your work yet?
To name the area in which progress is being made, the preposition 'in' with the dative is often used. Typical expressions are 'im Beruf weiterkommen' (to get ahead in one's career) or 'im Leben weiterkommen' (to get ahead in life).
Sie bildet sich ständig fort, weil sie in ihrem Job weiterkommen möchte.
She is constantly continuing her education because she wants to get ahead in her job.
When it is about solving a problem, 'weiterkommen' (to make progress) is very often used in the negative form. The problem itself is named with the preposition 'bei' (+ dative).
Ich komme bei dieser Übung einfach nicht weiter.
I just can't make any progress on this exercise.
In the context of competitions or sports, the next stage reached is often expressed with 'in' + accusative. For example: 'in die nächste Runde weiterkommen' (to advance to the next round) or 'ins Finale weiterkommen' (to advance to the final).
Die Favoritin ist souverän ins Halbfinale weitergekommen.
The favorite advanced confidently to the semifinal.
to get through
Durchkommen and weiterkommen can both express success in an exam or selection process. Durchkommen mainly means passing the exam or getting through the difficult process, while weiterkommen emphasizes reaching the next step or round. Use durchkommen for passing and weiterkommen for reaching the next stage.

Nach dem bestandenen Test ist Lara in die nächste Runde weitergekommen.
After passing the test, Lara advanced to the next round.
Obwohl die Prüfung schwierig war, ist Lara mit knapper Punktzahl durchgekommen.
Although the exam was difficult, Lara passed with only just enough points.