Question

The 20-inch-diameter wheels of one car travel at a rate of 24 revolutions per minute,

while the 30-inch-diameter wheels of another car travel at a rate of 18 revolutions per 
minute. What is the ratio of the speed of the second car to that of the first?

Answer 1

One revolution of a wheel is equal to it's circumference:

C = πd

C: circumference
d: diameter

20" wheel
d = 20"
C = (20π) in/rev
v = (24 rev/min)(20π in/rev) = 480π in/min

30" wheel
d = 24"
C = (30π) in/rev
v = (18 rev/min)(30π in/rev) = 540π in/min


`Ratio = (velocity of 30`


`(v_(2))/(v_(1)) = (540\pi)/(480\pi) = (9)/(8)`