In a certain gear, a bicycle tire with a diameter of 27 inches makes 3 complete revolution of the pedal.If a cyclist is pedaling at a rate of 100 revolutions per minute, find the speed of the bicycle in miles per hour?
To find the speed of the bicycle in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour.
First, let's determine the distance the bicycle travels in one revolution of the pedal:
The circumference of a circle is given by the formula C = π * d, where C is the circumference and d is the diameter. In this case, the diameter of the bicycle tire is 27 inches, so the circumference will be C = π * 27 inches.
Since the bicycle tire spins three times for every revolution of the pedal, the distance traveled in one revolution of the pedal is 3 times the circumference. Therefore, the distance traveled in one revolution of the pedal is D = 3 * C.
Now, let's find the distance traveled in one minute:
The cyclist is pedaling at a rate of 100 revolutions per minute, so the distance traveled in one minute is D_total = 100 * D.
Next, let's convert the distance from inches to miles:
We know that there are 12 inches in a foot and 5280 feet in a mile. Therefore, to convert from inches to miles, we divide the distance by (12 * 5280).
Finally, we convert the time from minutes to hours:
Since there are 60 minutes in an hour, we divide the distance by 60 to convert it to miles per hour.
Let's calculate the speed of the bicycle using these steps:
Assuming you meant
a bicycle tire makes 3 complete revolutions for each revolution of the pedal
then we have (in inches/minute)
100 * 3 * 27π
Now just convert that to miles/hour.