What would be the car's speed in miles per hour if its wheels are turning at 800 rpm?

Question

The wheel (including the tire) of the sports car has an 11-inch radius.

Answer 1

Since we are given that the tire is rolling at 800 rpm (revolution per minute), we first need to find out how long is a revolution. In one revolution, the tire advances one circumference. What is the circumference of a circle with radius 11 inches?

c = 2*π*r = 2*π*11 inches

In one minute, the tire revolves 800 times, so how far will the car go in 1 minute?

d = 800 * r = 800 * 2*π*11 inches

What will be the speed? Distance / time. Distance is 1600*π*11 inches and time is 1 minute. So, speed is

v = 1600*π*11 inches/minute. Now we need to convert this to miles / hour. How many minutes are in an hour? 60

1600*π*11 inches/minute * 60 minutes/hour = 1600*π*11*60 inches / hour (note that minutes canceled out)

How many inches are in a mile? First convert inches to feet. There are 12 inches in a feet. (1 ft = 12 inches. To convert inches to ft, we need to divide by inches and multiple by ft or multiply speed which is in inches / hour with 1 ft / 12 inches)

1600*π*11*60 inches / hour * 1 ft /12 inches = 1600*11*60/12 * π ft / hour = 1600*11*5*π ft / hour (note that inches canceled out)

How many ft is in a mile? 5280

1600*11*5*π ft / hour * 1 mile / 5280 ft = 16.67 miles / hour (note that ft canceled out)

Answer 2

The circumference of the wheel is d*pi=22*3.14=69.115".

69.115*800=55,292.2"/min.

5280*12=63,360"

55.292.2/63,360=.87266mpm*60=52.359mph

Answer 3

This problem requires a bunch of arithmetic...which you should be able to do.

The circumference of the wheel is 2π*11.inches

In each minute the wheel goes 1600*2π*11 inches

In each hour the wheel goes 96000*2π*11 inches, i.e. this is inches per hour.

Now just convert inches to miles.