Restrictions on validity
According to Downs, the link between average speeds on public transport and private transport applies only "to regions in which the vast majority of peak-hour commuting is done on rapid transit systems with separate rights of way. Central London is an example, since in 2001 around 85 percent of all morning peak-period commuters into that area used public transit (including 77 percent on separate rights of way) and only 11 percent used private cars. When peak-hour travel equilibrium has been reached between the subway system and the major commuting roads, then the travel time required for any given trip is roughly equal on both modes."[citation needed]
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So in general, it's entirely unclear whether this effect applies in most scenarios on the road network. In my area of NYC, a poster child for arguments about this effect and why we should never build anything due to "induced demand", it is vastly faster to drive across any borough other than Manhattan rather than taking public transit at all times except certain corridors at the absolute peak of rush hour.