Explanation:

- Option 1: "Though they worked" - This segment is correct. It uses the past tense "worked" appropriately to show action in the past.

- Option 2: "to build the highway" - This segment is also correct. The infinitive phrase "to build" is correctly structured.

- Option 3: "day and night" - This segment is correct as well. It's a common phrase to indicate working continuously.

- Option 4: "could not completed" - This segment is incorrect. The modal "could" should be followed by the base form of the verb, so it should be "could not complete" instead of "could not completed".