BTGmoderatorLU wrote: ↑

Fri Mar 05, 2021 3:20 am

Source: Manhattan Prep

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 centimeters 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. \(1280 \pi\)
B. \(75r\)
C. \(48r\)
D. \(24r\)
E. \(64\pi/3\)

The OA is B

Solution:

We can let x = the number of revolutions the smaller wheel makes per minute in order for the conveyor belt to work smoothly. Since the two wheels have to rotate the same distance in any given minute, we can create the equation:

π * 40 * r = π * 32 * x

Dividing both sides by 8π, we have:

5r = 4x

5r/4 = x

Therefore, the number of revolutions the smaller wheel makes per minute, in terms of r, is 5r/4, and in one hour, it can make 5r/4 * 60 = 75r revolutions.

Answer: B