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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 :

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

[tex]Ratio = \frac{velocity of 30" wheel}{velocity of 20" wheel} = \frac{v_{2}}{v_{1}}[/tex]

[tex]\frac{v_{2}}{v_{1}} = \frac{540\pi}{480\pi} = \frac{9}{8}[/tex]












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