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math

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One wheel has a diameter of 30 inches and a second wheel has a diameter of 20 inches. The first wheel traveled a certain distance in 240 revolutions. In how many revolutions did the second wheel travel the same distance?

not just an answer please

A.120
B.160
C.360
D.420
E.480

  • math -

    short way:
    the number of revolutions varies inversely with the diameter of the wheel
    i.e. the larger the wheel the smaller the number of revs.

    R1/R2 = C2/C1
    240/R2 = 20/30
    20R2 = 7200
    R2 = 360

    or

    distance covered by first wheel = 2π(15)(240) = 7200π inches

    circumference of 2nd wheel = 2π(10) = 20π inches
    for the same distance of 7200π inches
    number of revolutions = 7200π/(20π) = 360 revs

  • math -

    c.360

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