Revolutions problem

[infiniti007]

Can anybody shed light on how to solve this problem algebraically?



The diagram above shows two wheels that drive a conveyor belt. The larger wheel has a diameter of 40 centimeters, and the smaller wheel has a diameter of 32 centimeters. If each wheel must rotate the exact same number of centimeters per minute, and the larger wheel makes r revolutions per minute, then in terms of r, how many revolutions does the smaller wheel make per hour?

A) 1,280Ï€ / 3
B) 75r
C) 48r
D) 24r
E) 64Ï€ / 3

[GMATGuruNY]

The diagram above shows two wheels that drive a conveyor belt. The larger wheel has a diameter of 40 centimeters, and the smaller wheel has a diameter of 32 centimeters. If each wheel must rotate the exact same number of centimeters per minute, and the larger wheel makes r revolutions per minute, then in terms of r, how many revolutions does the smaller wheel make per hour?

A) 1,280Ï€ / 3
B) 75r
C) 48r
D) 24r
E) 64Ï€ / 3

Revolutions per minute = (distance rotated each minute)/(circumference).

Big diameter : small diameter = 40:32 = 5:4.
Since circumference = πd, we get:
Big circumference : small circumference = 5Ï€ : 4Ï€.

To make the math easier, we can use these smaller values -- 5Ï€ and 4Ï€ -- to determine how many revolutions are made by the small wheel for every revolution made by the big wheel.
Let the distance rotated each minute = the LCM of 5Ï€ and 4Ï€ = 20Ï€ centimeters.

Big wheel's revolutions per minute = r = (20Ï€)/(5Ï€) = 4.
Small wheel's revolutions per minute = (20Ï€)/(4Ï€) = 5.
Thus:
Small wheel's revolutions per 60 minutes = 60*5 = 300. This is our target.

Now plug r=4 into the answers to see which yields our target of 300.
Only B works:
75r = 75*4 = 300.

The correct answer is B.

[nikhilgmat31]

answer is B.