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Algebra/geometry question problem... Explian

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Algebra/geometry question problem... Explian

by dinesh19aug » Wed Aug 25, 2010 6:37 pm
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

Can some one please xplain... How to solve this problem.
Source - GmatClub test


ANS D
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by Rahul@gurome » Wed Aug 25, 2010 7:42 pm
Solution:
Engine or the smaller wheel 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.
Radius of smaller wheel is 2.
Or its circumference is 2*pi*2 = 4*pi.
Let the radius of mixing wheel 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.

The correct answer is hence (D).
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