This is the 17870th most frequent Russian word.
успеют
"Успеют" means "they will manage (to do something) in time" or "they will succeed."
In this sentence, 'успеют' signifies the action of being able to complete, specifically reaching the meeting on time, indicating assurance or prediction of success.
Они успеют прибежать к началу встречи.
They will manage to arrive at the start of the meeting.
Here, 'успеем' demonstrates the idea of succeeding in catching the train through timely action, dependent on the condition of hurrying.
Если мы поторопимся, мы успеем на поезд.
If we hurry, we will catch the train.
In this example, 'успеют' is used to express the potential of not completing the project within the specified time limit, showing doubt or concern.