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The sentence is correct because you are describing a situation that took place over a period of time.
You may be thinking of contrasting "could" in the past with "was able to." "Could" to refer to one past event that happened finally is not correct. For example, we would not say, "After waiting in line for five hours, we could get tickets for the concert." We would have to say here, "After waiting in line for five hours, we were able to get tickets for the concert."
Your sentence is correct because it most likely refers to an ability to perform something over a period of time. The sentence, for example, might come from a passage like this:
"¢ Life was better in the old days. My father and his brother lived in the country, where there were country roads and no traffic. The brothers could often bike to school when they were young. That is not the case now. Children can't bike to school any more because the area is criss-crossed by Interstate highways, and the traffic is very heavy. Children have to go to school by car and bus now.
See these discussions of "could" in the past tense on the Grammar Exchange: