If it would take one machine 10 minutes to fill a large production ord

Question

If it would take one machine 10 minutes to fill a large production order and another machine 12 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?

A. 4 1/60
B. 5
C. 5 5/11
D. 5 1/2
E. 11

PS21161

A. 4 1/60 
B. 5 
C. 5 5/11 
D. 5 1/2 
E. 11

PS21161

Icecream87 · Answer

C
the total rate : 1/10 + 1/12 = 11/60
Work/Rate = 1*60/11 or 5 5/11

Abhishek009 · Answer

Let the total production order be of 60 units

1^{st}  machine can fill the production order at 6 units per minute

2^{nd}  machine can fill the production order at 5 units per minute

So,  1^{st}  and  2^{nd}  machine working togather can fill the production order at 11 units per minute

The total production order is of 60 units so the time taken to complete the order is -  \frac{60}{5}  =  5 \frac{5}{11}  minutes

Hence answer is (C) ,  5 \frac{5}{11}  minutes

Skywalker18 · Answer

Since , Machine 1-M1 take 10 mins to fill the order
The work done by M1 in a min = 1/10
Machine 2- M2 take 12 mins to fill the same order
and work done by M2 in a min = 1/12

Total work done by M1 and M2 in a min = 1/10 + 1/12 = 11/60
Time needed for M1 and M2 to complete the order = 60/11 = 5 5/11

Answer C

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual completion rates of the respective entities (for the same job).

We're told that one machine takes 10 minutes to complete a job and another machine takes 12 minutes to complete the same job. Plugging in those values gets us...

(10)(12)/(10+12) = 120/22 = 5 10/22 = 5 5/11 minutes

Final Answer:  C

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

BrentGMATPrepNow · Answer

With most work questions, a useful approach is to  assign a "nice" value  to the total job. 
We want a number that works well with the given numbers, 10 and 12

So, let's say the production order consists of making   120   widgets

It would take one machine 10 minutes to fill the production order  
Rate = output/ time =   120  /10 = 12 widgets per minute

It would take the other machine 12 minutes to fill the production order  
Rate = output/ time =   120  /12 = 10 widgets per minute

COMBINED rate of both machines = 12 + 10 =  22  widgets per minute

How many minutes would it take both machines working together, at their respective rates, to fill the order?  
Time = output/rate =   120  / 22  = 60/11 =  5 5/11 minutes

Answer: C

Cheers,
Brent

Abhishek009 · Answer

FORMULA APPROACH

\frac{10*12}{10+12} = \frac{120}{22} => \frac{60}{11} = 5\frac{5}{11} , Answer must be (C)

DanTheGMATMan · Answer

Bread and butter rate question:

https://www.youtube.com/watch?v=Hd4CsuidH8g

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