Final answer:
To determine the bicycle speed, calculate the rear wheel's circumference, use the gear ratio to find the rear wheel's rotation rate, and then convert the distance traveled per second into miles per hour. The resulting speed is 17.3 mph when pedaling at 1.1 revolutions per second.
Step-by-step explanation:
The student's question involves calculating the speed of a bicycle based on the diameters of the sprockets on the pedal and rear wheel, the diameter of the rear wheel, and the pedaling rate in revolutions per second. To find the speed in miles per hour, we first calculate the circumference of the rear wheel, which gives us the distance traveled per revolution. We then use the gear ratio to find the effective revolutions of the rear wheel based on the pedaling speed. The total distance traveled per second is then converted to miles per hour.
The diameter of the rear wheel is 26 inches, so its circumference is π(26 inches) ≈ 81.68 inches. The gear ratio is the diameter of the pedal sprocket (6 inches) over the diameter of the rear wheel sprocket (4 inches), giving us a 1.5:1 gear ratio. For every pedal revolution, the rear wheel rotates 1.5 times. Pedaling at 1.1 revolutions per second, the rear wheel rotates at 1.5 * 1.1 = 1.65 revolutions per second. The distance traveled per second is then 81.68 inches * 1.65 ≈ 134.77 inches per second.
To convert inches per second to miles per hour, we use the conversion factors 12 inches per foot and 5280 feet per mile, and 3600 seconds per hour. Thus, the bike speed is (134.77 inches/second) * (1 foot/12 inches) * (1 mile/5280 feet) * (3600 seconds/hour) ≈ 17.26 miles per hour. Rounded to the nearest tenth, the bicycle is traveling at 17.3 mph.