Mach 0.89 Which is also 677 MPH
Actually it's cruise speed was originally supposed to be Mach 0.89 as the 7E7, as the 787 it is Mach 0.85. Basically 5% faster then the 767 and most airliners, and 20% less fuel burn. Other interesting points are it is composite, which gives some great benefits for passengers.
It's way easier on your ears as it can pressurize 60% higher, much better when you have a cold or sensitive ear canals.
One of the other stress's of today's jet traveler, all the air is humidified so much less dehydration. Other metal aircraft don't do this.
Turbulence is minimized by a state of the art turbulence mitigation system.
The crusing speed of a Boeing 787 is:
Mach 0.85 / 567 mph / 490 knots or 913 km/h.
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