Question

Every time the pedals go through at 360° rotation on certain bicycle, the tires will rotate three times. If the tires are 24 inches in diameter, what is the minimum number of complete rotation of the pedals needed for the bicycle to travel at least 1 mile?

Answer 1

281 rotations of the pedals

Explanation:

first use the diameter of the tire given to find the circumference of the wheel, so that we know how far the bicycle travels for each rotation of the wheel:

C=2(pi)(r)

C=2(pi)(24/2)

C=24(pi)

C=about 75.4

so the bike travels 75.4 for every rotation of the wheel

there are 63360 inches in a mile

so divide the number of inches in a mile by the number of inches the bike moves for ever rotation of the wheel to find how many rotations of the wheel it takes to travel a mile:

63360/75.4=840.3

now, this is the number of rotations of the WHEEL we need to find rotations of the pedals. if the tires rotate 3 times for every one rotation of the pedals, then divide 840.3 by 3 to find how many rotations of the pedals it will take for the wheels to travel a mile

840.3/3= about 280.1 rotations of the pedals, which rounds to 281 for complete rotations

Answer 2

281 complete rotations

Explanation:

One mile is equal to 5280 feet or 63360 inches. The circumference of the tire is given by:

C = πd

C = π × 24 inches

C = 75.398 inches

For each rotation of the pedals, the tire rotates 3 times. Therefore, the distance covered by the bicycle for each rotation of the pedals is:

distance per rotation = 3 × C

distance per rotation = 3 × 75.398 inches

distance per rotation = 226.194 inches

To cover at least 1 mile, the bicycle needs to travel:

distance to travel = 63360 inches

The minimum number of complete rotations of the pedals needed is:

number of rotations = distance to travel / distance per rotation

number of rotations = 63360 inches / 226.194 inches

number of rotations ≈ 280.04 rotations

Since the number of rotations must be a whole number, the bicycle needs to make at least 281 complete rotations of the pedals to travel at least 1 mile.