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# A bicycle with two wheels of different sizes moves at 3 meters per sec

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Math Expert
Joined: 02 Sep 2009
Posts: 50619
A bicycle with two wheels of different sizes moves at 3 meters per sec  [#permalink]

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14 Sep 2018, 00:45
00:00

Difficulty:

65% (hard)

Question Stats:

38% (01:50) correct 62% (01:40) wrong based on 21 sessions

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A bicycle with two wheels of different sizes moves at 3 meters per second, at how many rotations per second does the smaller wheel rotate?

(1) The smaller wheel is 0.5 m wide in diameter.
(2) The larger wheel is twice as wide in diameter, and rotates at $$\frac{3}{\pi}$$ rotations per second.

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Re: A bicycle with two wheels of different sizes moves at 3 meters per sec  [#permalink]

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15 Sep 2018, 05:21
Bunuel wrote:
A bicycle with two wheels of different sizes moves at 3 meters per second, at how many rotations per second does the smaller wheel rotate?

(1) The smaller wheel is 0.5 m wide in diameter.
(2) The larger wheel is twice as wide in diameter, and rotates at $$\frac{3}{\pi}$$ rotations per second.

For two wheels of different diameters

Ratio of revolutions, $$R_1 / R_2 = D_2 / D_1$$ where $$D_1$$ and $$D_2$$ are diameters of the wheels

Question: at how many rotations per second does the smaller wheel rotate?

Statement 1: The smaller wheel is 0.5 m wide in diameter.
The distance travelled in 1 sec by smaller wheel = 3 meters
Distance travelled by small wheel in one revolution = $$0.5π$$
Number of revolutions per second = $$3/(0.5π)$$
SUFFICIENT

Statement 2: The larger wheel is twice as wide in diameter, and rotates at $$\frac{3}{\pi}$$ rotations per second..
Now we cam calculate the rotation of bigger wheel as well as smaller wheel just like we did in first statement hence
SUFFICIENT

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Re: A bicycle with two wheels of different sizes moves at 3 meters per sec &nbs [#permalink] 15 Sep 2018, 05:21
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