macjas wrote:

Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?

A. 1280π

B. 75r

C. 48r

D. 24r

E. (64π)/3

1. Let the number of revolutions made by the smaller wheel in 1 hr be s

2. Given: Number of centimeters rotated by both the wheels in 1 hr is the same

3. Number of centimeters rotated by the larger wheel in one revolution = its circumference=2*pi*20=40Pi

4. Number of centimeters rotated by the larger wheel in 1 hr = 40*pi*60*r

5. Number of centimeters rotated by the smaller wheel in one revolution=its circumference=2*pi*16=32*pi

6.Number of centimeters rotated by the smaller wheel in 1 hr= 32*pi*s

7. Equating (4) and (6) based on (2),

40*pi*60*r = 32*pi*s

i.e., s= 75r

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