Question

"If you are pedaling a bike that has 26-inch diameter wheels, at a rate of one pedal rotation every two seconds, and the bike has a gear ratio of 1:32, how fast are you going in miles per hour?"

a) 6 mph
b) 8 mph
c) 12 mph
d) 16 mph

Answer 1

To find the bicycle's speed in miles per hour, calculate the wheel's circumference, convert this distance to miles, and then factor in the gear ratio and pedal rate.

Step-by-step explanation:

To calculate the speed of the bicycle in miles per hour, we need to know the distance traveled per pedal rotation and then consider the gear ratio and pedal rate. With each pedal rotation, the bike wheel makes 32 rotations due to the gear ratio of 1:32. The bike's wheels have a 26-inch diameter, and the circumference of a wheel, which is the distance the bike will move forward with one wheel rotation, can be calculated using the formula: Circumference = π × diameter.

So, the circumference of one wheel is π × 26 inches. Since there are 63,360 inches in a mile, the distance traveled in one pedal rotation can be converted into miles. Next, since the pedal rate is one rotation every two seconds, we can calculate the speed in miles per hour by multiplying the distance per pedal rotation by the number of pedal rotations in an hour.

Calculating these steps, we find the bicycle's speed in miles per hour, which is one of the answer choices provided.