die Strecke
distance
A defined route or distance between two points that is covered.
Die Strecke von hier zum Bahnhof beträgt etwa zwei Kilometer.
The distance from here to the train station is about two kilometers.

route / distance
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distance
A defined route or distance between two points that is covered.
Die Strecke von hier zum Bahnhof beträgt etwa zwei Kilometer.
The distance from here to the train station is about two kilometers.

The noun 'die Strecke' (route/distance) is related to the verb 'strecken' (to stretch). Figuratively speaking, a Strecke is a 'stretched' path from one point to another.
Die Katze streckte sich genüsslich in der Sonne.
The cat stretched itself contentedly in the sun.
'Strecke' is often combined with verbs of movement. Typical phrases are 'eine Strecke zurücklegen' (to cover a distance), 'eine Strecke fahren' (to travel/drive a route), or 'eine Strecke laufen' (to run/walk a distance).
Für den Marathon müssen die Läufer eine Strecke von über 42 Kilometern zurücklegen.
For the marathon, the runners have to cover a distance of over 42 kilometers.
The idiom 'auf der Strecke bleiben' is a fixed unit. Metaphorically, it means that someone or something fails, gives up, or can no longer keep up.
Bei der schnellen Entwicklung des Projekts sind einige ursprüngliche Ziele auf der Strecke geblieben.
During the rapid development of the project, some original goals fell by the wayside.
This meaning of 'Strecke' is a technical term from hunting language. Outside the topic of hunting, you will hardly hear or read this meaning.
Am Ende der Jagd legten die Jäger die Strecke.
At the end of the hunt, the hunters laid out the bag.
piece
'das Stück' and 'die Strecke' can both have to do with a path or route. 'die Strecke' means the route or distance between two points, for example when driving, running, or traveling. 'ein Stück' means only part of this route and often sounds a little less precise or more everyday. You can say: 'Ich gehe ein Stück mit dir' (I'll walk part of the way with you), but for the exact route or distance, you are more likely to say 'Strecke'. The words can be confused because both can describe part of a route. 'Strecke' is more precise; 'Stück' is more casual.

Die Strecke bis zum Bahnhof ist kurz, aber es geht die ganze Zeit bergauf.
The distance to the station is short, but it goes uphill the whole way.
Nach dem Essen gingen wir noch ein Stück am Fluss entlang.
After the meal, we walked a little way along the river.