If a bicycle has a crankshaft of 40 teeth, and there are three rear sprockets attached to the rear wheel, 20 teeth, 16 teeth and 12 teeth. The diameter of the rear wheel is 60 cm. Which sprocket should be used to get the most distance in one paddle? What would the distance be?

To determine which sprocket should be used to achieve the most distance in one pedal stroke, we need to consider the gear ratio of each combination and calculate the distance covered by each.

First, let's calculate the gear ratio for each sprocket:

Gear ratio = Number of teeth on the front crankshaft / Number of teeth on the rear sprocket

For the 20-tooth rear sprocket:
Gear ratio = 40 teeth / 20 teeth = 2

For the 16-tooth rear sprocket:
Gear ratio = 40 teeth / 16 teeth = 2.5

For the 12-tooth rear sprocket:
Gear ratio = 40 teeth / 12 teeth = 3.33 (rounded to two decimal places)

The gear ratio represents the number of wheel rotations for one full rotation of the crankshaft. To calculate the distance covered in one pedal stroke, we need to consider the circumference of the rear wheel.

Circumference of the wheel = π * diameter
Circumference = 3.14 * 60 cm = 188.4 cm (rounded to one decimal place)

Now, suppose one full rotation of the crankshaft is performed, we need to calculate how much distance is covered for each sprocket:

Distance covered = Gear ratio * Circumference

For the 20-tooth rear sprocket:
Distance covered = 2 * 188.4 cm = 376.8 cm or 3.77 meters

For the 16-tooth rear sprocket:
Distance covered = 2.5 * 188.4 cm = 471 cm or 4.71 meters

For the 12-tooth rear sprocket:
Distance covered = 3.33 * 188.4 cm = 627.012 cm or 6.27 meters (rounded to two decimal places)

Therefore, the sprocket with 12 teeth should be used to achieve the most distance in one pedal stroke, covering approximately 6.27 meters.