to keep up
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to keep up
To reach or maintain the same pace, level, or performance as someone else.
Obwohl er älter ist, kann er beim Laufen immer noch mit den Jüngeren mithalten.
Although he is older, he can still keep up with the younger people when running.
to join in
To take part in an activity, competition, or undertaking; to join in.
Als es darum ging, für den guten Zweck zu spenden, wollten alle mithalten.
When it came to donating to a good cause, everyone wanted to join in.
'Mithalten' (to keep up) is a separable verb. The prefix 'mit-' comes at the end in a main clause, stays attached to the verb in subordinate clauses, and in the infinitive with 'zu', 'zu' goes in the middle.
Bei diesem schnellen Tempo halte ich nicht mit.
I can't keep up at this fast pace.
The verb is made up of 'mit' (with) and 'halten' (to hold). The literal idea is that you 'hold' yourself at the same level 'with' others.
Ich kann bei den Kosten für dieses Hobby einfach nicht mehr mithalten.
I simply can't keep up with the costs of this hobby anymore.
If you want to say who or what you are keeping up with, you use the preposition 'mit' followed by the dative.
Sie kann problemlos mit den besten Studenten der Klasse mithalten.
She can easily keep up with the best students in the class.
Common expressions are 'nicht mehr mithalten können' (to no longer be able to keep up), when someone is overwhelmed, or 'im Tempo mithalten' (to keep up with the pace), when it is about speed.
Der kleine Laden konnte mit den Preisen der großen Supermärkte nicht mithalten.
The small shop couldn't keep up with the prices of the large supermarkets.
to arrive
Both words can express comparable performance against an opponent. Mithalten emphasizes reaching or maintaining the same pace or level. Gegen jemanden ankommen can mean the same thing, but focuses more strongly on whether you can hold your own against or prevail over the opponent.
Über weite Strecken kann Lea mit der Meisterin gut mithalten.
Lea can keep up well with the champion for much of the match.
Im entscheidenden Satz kommt Lea gegen die Meisterin nicht an.
Lea can't hold her own against the champion in the decisive set.
