A factory worker operates a machine that processes metal rods.

Question

A factory worker operates a machine that processes metal rods. The machine takes  4  hours to complete a batch of  6  rods, but due to an efficiency boost, it can process the same number of rods in  2  hours on the return cycle. What is the average processing rate, in rods per hour, for the entire cycle?

(A)  2  
(B)  3  
(C)  3.2  
(D)  3.6  
(E)  4

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ManifestDreamMBA · Answer

Total rods being processed = 6*2 = 12
Total time = 4+2 = 6

Ravg = 12/6 = 2

sachbash14 · Answer

First cycle
W = R*T
6 = R*4
R = 6/4

Return cycle
W = R*T
6 = R*2
R = 6/2 = 3

Average Processing Rate = Total Work / Total Time
 = (6+6) / (4+2)
= 12 / 6
= 2

kingbucky · Answer

Let’s solve this by organizing the data in a table to find the average processing rate for the entire cycle.

Cycle  
  To Cycle  
  Return Cycle  
  Entire Cycle (To + Return)  
 
   Time (hours)  
 4 
 2 
 4 + 2 = 6 
 
   Number of Rods  
 6 
 6 
 6 + 6 = 12 
 
   Rate (rods/hour)  
  \frac{6}{4} = 1.5  
  \frac{6}{2} = 3  
  \frac{12}{6} = 2

The average processing rate for the entire cycle is the total number of rods divided by the total time.  
  This gives us:  
 	ext{Average Rate} = \frac{	ext{Total Rods}}{	ext{Total Time}} = \frac{12}{6} = 2 	ext{ rods per hour} 
  
The average rate for the entire cycle is 2 rods/hour.

A factory worker operates a machine that processes metal rods.

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Cycle	To Cycle	Return Cycle	Entire Cycle (To + Return)
Time (hours)	4	2	4 + 2 = 6
Number of Rods	6	6	6 + 6 = 12
Rate (rods/hour)	\(\frac{6}{4} = 1.5\)	\(\frac{6}{2} = 3\)	\(\frac{12}{6} = 2\)

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A factory worker operates a machine that processes metal rods.

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