The wheels of a moving bicycle have 27-inch diameters, and they are spinning at 200 revolutions per minute. How fast is the bike traveling in miles per hour?

27*π*200=16964.6
1mi=63360in 63360/16964.6=3.73

I am not sure if i did it right

You figured out miles per minute, not mph, right?

You figured out min/mile. Keep track of the units!

16964.6 in/min * 1mi/63360in = 0.2677 mi/min

Now multiply that by 60min/hr to get mi/hr.

so i divide it by 60?

Well, I hate to burst your bubble, but your calculation seems a bit off. Let’s take it one step at a time and figure this out!

First, let's find the circumference of the bicycle wheel. The formula for the circumference is C = πd (C = Circumference, π = Pi, d = Diameter).

So, the circumference of a wheel with a 27-inch diameter would be 27π, which is around 84.78 inches.

Now, to find how far the bike travels in one minute, we multiply the circumference by the number of revolutions per minute. In this case, it's 84.78 inches * 200 revolutions, which equals 16,956 inches per minute.

To convert that to miles, we need to divide by the number of inches in a mile, which is 63,360 inches. So, 16,956 inches / 63,360 inches per mile gives us approximately 0.267 miles per minute.

Now, if you want to find the speed in miles per hour, we just need to multiply the speed in miles per minute by 60 (since there are 60 minutes in an hour). Therefore, 0.267 miles per minute * 60 minutes equals around 16.02 miles per hour.

So, to answer your question, the bike is traveling at approximately 16.02 miles per hour.

Don't worry about making mistakes; it happens to the best of us. I'm here to help clarify things and bring some laughter along the way!

To calculate the speed of the bike in miles per hour, we can use the following steps:

1. Calculate the circumference of the wheel: The circumference of a circle can be found using the formula C = π * d, where C is the circumference and d is the diameter. In this case, the diameter of the wheel is given as 27 inches, so the circumference is 27 * π inches.

2. Calculate the distance traveled in one revolution: Since the circumference represents the distance traveled in one complete revolution of the wheel, we can use this value to calculate the distance traveled in one revolution.

3. Multiply the distance traveled in one revolution by the number of revolutions per minute: By multiplying the distance traveled in one revolution by the number of revolutions per minute, we can find the total distance traveled in inches per minute.

4. Convert the total distance traveled from inches to miles: Since we want the speed in miles per hour, we need to convert the total distance traveled from inches to miles. There are 63,360 inches in a mile.

5. Convert the speed from minutes to hours: Lastly, we need to convert the speed from minutes to hours. There are 60 minutes in an hour.

Now let's go through the calculation:

1. Circumference of the wheel = 27 * π inches ≈ 84.823 inches (rounded to three decimal places)

2. Distance traveled in one revolution = 84.823 inches

3. Total distance traveled in one minute = Distance traveled in one revolution * number of revolutions per minute = 84.823 inches * 200 revolutions = 16,964.6 inches per minute

4. Total distance traveled in one minute = 16,964.6 inches per minute / 63,360 inches per mile ≈ 0.267 miles per minute (rounded to three decimal places)

5. Speed in miles per hour = 0.267 miles per minute * 60 minutes per hour ≈ 16.02 miles per hour (rounded to two decimal places)

Therefore, the speed of the bike is approximately 16.02 miles per hour.