Question

The radius of a car wheel is 14 inches. how many revolutions per minute is the wheel making when the car is traveling at 60 mph. round your answer to the nearest revolution?

Answer 1

Answer:

$721\ \frac{rev}{min}$

Step-by-step explanation:

step 1

Find the circumference of the wheel

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=14\ in$

substitute

$C=2\pi(14)$

$C=28\pi\ in$

assume

$\pi=3.14$

$C=28(3.14)=87.92\ in$

step 2

$1\ mile=63,360\ inches$

$1\ hour=60\ minutes$

we have that

The speed of the car is 60 miles/hour

Convert the speed to inches/minute

$60\ \frac{mi}{h}=60(\frac{63,360}{60})=63,360\ \frac{in}{min}$

step 3

Remember that

The circumference of the wheel subtends one revolution

so

$1\ rev=87.92\ in$

Convert the speed to rev/min

$63,360\ \frac{in}{min}=\frac{63,360}{87.92}=721\ \frac{rev}{min}$