bblast wrote:A machine consisting of 3 connected wheels is mixing concrete. The engine is running at a speed of 60 rpm and the mixer is mixing at a rate of 8 rpm. If the radius of the smaller (drive) wheel is 2 inches, what is the diameter of the mixing wheel? The smaller wheel is driven directly by the engine.

12
15
25
30
32

D

Radius of mixing wheel= (60 x 2)/8 = 15 inch
hence Diameter = 30 inch

Anser is D

Since the smaller circle has radius of 2 then its perimeter is 4Ï€

every minute it goes a way of 4Ï€*60 = 240Ï€

the biggest circle perimeter is unknown 2*Ï€*r

240*Ï€ = 2*Ï€*r*8

r = 15

so the diameter is 30.

Smaller wheel/engine is running at the speed of 60 rotations per minute.
60 rotations means it is covering its circumference 60 times in 1 minute. So it covers its circumference once in 1/60 minutes. And radius of smaller wheel is 2.
Or its circumference is 2*pi*2 = 4*pi.
Assume radius to be r.
So its circumference is 2*pi*r = 2r*pi.
The mixer is mixing at the speed of 8 rotations per minute. Or it is covering its circumference 8 times in 1 minute. So it covers its circumference once in 1/8 minutes.
So 4*pi : 2r*pi = 1/60 : 1/8.
Or 2r/60 = 4/8.
Or r = 15.
Or diameter is 2*r = 30.

Right Choice (D).