>

compared to off peak hours, when there are less services
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Depends what kind of public transport, could be that motorcycle would get you there faster (been there, done that). >

*In a city...
Where I live, there is no route a bus takes that is quicker than driving. Trains take longer too as the train station is too far from the town centres / places I want to go
Edit to add: no subway / trams / etc - do airplanes count? >

Not where I live, busses and streetcars use the same roads as cars, and subways still require getting on said busses and walking...if they aren't full. There's also biking. >

key word faster
bikes tend to take similar amounts of time whether or not its peak time >

You mean they're faster than themselves?! They aren't, for said reasons. Subways would be the same in that case.