Answer:
19.2 mph
Step-by-step explanation:
Given a bike wheel with a radius of 21 inches turning at 154 rpm, you want to know the speed of the bike in miles per hour.
Distance
A wheel with a radius of 21 inches will have a diameter of 42 inches, or 3.5 feet. In one turn, it will travel ...
C = πd
C = π(3.5 ft) . . . . per revolution
In one minute, the bike travels this distance 154 times, so a distance of ...
(3.5π ft/rev)(154 rev/min) = 1693.318 ft
Speed
The speed is the distance divided by the time:
(1693.318 ft)/(1/60 h) × (1 mi)/(5280 ft) ≈ 19.2 mi/h
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Additional comment
We could use the conversion factor 88 ft/min = 1 mi/h.
Bike wheel diameters are typically 26 inches or less, perhaps 29 inches for road racing. A 42-inch wheel would be unusually large.
On the other hand, the chainless "penny farthing" bicycle has a wheel diameter typically 44-60 inches. It would be real work to pedal that at 154 RPM.
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