Random Pack 1, Question 2 An assembly line produces 40 cogs per hour

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QUANT 4-PACK SERIES Problem Solving Pack 1 Question 2 At a company meeting...

An assembly line produces 40 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the average output, in cogs per hour, for the assembly line during this time?

A) 42
B) 45
C) 48
D) 50
E) 55

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This question is part of the Quant 4-Pack series

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ENGRTOMBA2018 · Answer

Initial conditions:

40 cogs/h for 60 cogs --> total time to produce 60 cogs = 60/40 = 1.5 hours.

After ramping up the production, 60 cogs/ hour for 60 cogs ---> 1 hour more.

Total time = 1.5+1 = 2.5 hours, producing 60+60 = 120 cogs,

Thus the average output = 120/2.5 = 48 cogs/hour. C is the correct answer.

EMPOWERgmatRichC · Answer

Hi All,

This question revolves around rates and average overall rates, so it can be treated the same way that you would treat an Average Speed question. To determine the average output per hour, we need to know the total cogs produced and the total time spent producing those cogs.

For the first part of the order, we know the rate (40 cogs/hour) and the total produced (60 cogs), so we can figure out the amount of time...

Total Cogs = (Production Rate)(Time)
60 cogs = (40 cogs/hr)(T hours)
60/40 = T
1.5 hours = T

For the second part of the order, we have the same types of information to work with (60 cogs/hr and 60 cogs produced)....

Total Cogs = (Production Rate)(Time)
60 cogs = (60 cogs/hr)(T hours)
60/60 = T
1 hour = T

With the TOTAL COGS (60 + 60 = 120 cogs) and the TOTAL TIME (1.5 + 1 = 2.5 hours), we can now calculate the AVERAGE production rate, in cogs per hour, for the assembly line:

Total Cogs = (Production Rate)(Total Time)
120 cogs = (Rate)(2.5 hours)
120/2.5 = Rate
48 cogs/hour = R

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

sanguine31 · Answer

First rate = 40cogs/hr till 60 cogs are produced 
So n1=60, t1=60/40=1.5 hrs

Second rate = 60 cogs/hr till another 60 cogs are produced.
So n2=60, t2=60/60=1 hr.

In total the average no. of cogs produced per hour = \frac{total no. of cogs}{Total no. of hours} 
 = \frac{120}{2.5} 
 =48 cogs/hr

arhumsid · Answer

As soon as you realize its testing the Rates/Distance basics, it becomes quite trivial. 
Just translate in terms of Speed and Distance:
 Speed1 : 40 cogs/hr
Distance1: 60 Cogs

Spped2: 60 cogs/hr
Distance2: 60 cogs

Avg speed (when distances are same)  :  \frac{2*S1*S2}{S1+S2} 
 => \frac{2*40*60}{40+60} 
 => 48 cogs/hr

Option C

Please let me know if im wrong.

Abhishek009 · Answer

Hour 1 = 40 cogs 
Hour 1 \frac{1}{2}  = 60 cogs

Hour 2 \frac{1}{2}  = 60 cogs

Hence after 2 \frac{1}{2}  from starting 120 cogs are produced.

Average cogs produced per Hour = Total No of cogs produced/Time from starting production

Average cogs produced per Hour = 120/2 \frac{1}{2}  => 48 cogs per hour.

A) 42
B) 45
C) 48
D) 50
E) 55
  
Hence answer is (C)

KrishnakumarKA1 · Answer

with 40 cogs/hr, to produce 60 cogs, time taken is 60/40 = 1.5 hrs
with 60 cogs/hr, to produce 60 cogs, time taken is 60/60 = 1 hrs

Total time taken is 1.5 +1 = 2.5
total cogs produced = 120

average rate = 120/2.5 =48 cogs/hr

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Random Pack 1, Question 2 An assembly line produces 40 cogs per hour

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