The photo was taken in 1888 in front of the Smithsonian Institution's "Castle" on the Mall. The driver is Lucius D. Copeland, who invented the device (30 mile range, 10 mph). His passenger is Frances "Fannie" Benjamin Johnston, later to become one of Washington's most famous photographers.
The steam-powered tricycle was much more practical than its French predecessor, the dog-powered tricycle.
Photo credit to the Smithsonian Institution Archives, via.