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As far as I know, Google Maps give different estimated arrival time at different time. For example, at midnight the estimated arrival time lower than usual because of less traffic at that time.

I want to know at what time (in average) Google Maps give the highest estimated arrival time?

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    From where? To where? With which mode of transport? – Henning Makholm Apr 21 at 9:06
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    It will probably depend a lot on the itinerary and the local traffic patterns. The longest travel time will be related to peak traffic periods, which will be in the morning and late afternoon usually. – jcaron Apr 21 at 9:07
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Usually the expected time of arrival will get later when you hit peak hour, getting highest when you go the same direction as most of the traffic and as such meeting the most traffic jams.

These will be adding more time in cities with bad traffic flow.

It will not be one given time for all of a country/time zone and even less for all the world.
There will be different times for different cities and different directions of travel. Into a big city in the morning will usually be much longer than traveling out of the same city.

Worse may be if you have a ferry that has big gaps in its schedule. Like to an island which has a break for the night, so if you would arrive just after the last ferry of the day the expected time of arrival will be after the first ferry the next day, if you do not get a 'can not calculate' message.

If there are special circumstances, like road closures due to work that change the averages and road closures due to accidents that change it for 'travel now' calculations.

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Since the start and end points weren't specified, the highest estimated time I could find is 342 hours from Aasfontein, South Africa to Talon, Magadan Oblast, Russia. I don't think this one varies much by time of day.

EDIT: Found a longer one: 458 hours from Kumana, Sri Lanka to Asike, Indonesia, although more than half the time is on ferries.

Disclaimer: Of course my literal interpretation of the question "What time is the highest Google Maps estimated arrival time?" is probably not what OP was actually looking for.

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    I think the OP was asking about the longest times of day for a given route, not the world's longest route. – jpatokal Apr 21 at 10:02
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    That is the highest (car journey I presume) total travel time. I read the question as asking for the highest different based on the time of day. – Willeke Apr 21 at 10:02

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