How do international flights make up for lost time in case of delay in departure?

I've seen that intl flights can easily start an hour and a half after scheduled departure time and still arrive on time. I read somewhere it has something to do with flying at different altitudes, but I am not clear.
pilots can do things to make up time, flying at a higher altitude may be one of those things because the air is more thin and the plane can go more quickly. What happens most often though is that the time that is given to passengers as the time in route allows for delays that may result from airport congestion, weather, etc. If the flight typically has a strong headwind it is calculated into the transit time, but the weather may be different that day.

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